ArithRand - Arithmetic Randomness

Arithmetic Randomness

Project

The aim of the Austrian-French joint project ArithRand ("Arithmetic Randomness", 2021-2025) is to make progress on various questions that interrelate and link the notion of randomness (or pseudo-randomness) with the notion of determinism in the context of analytic number theory, combinatorics on words, automata theory, quasi-random sequences and nearby disciplines. It is financially supported by the FWF (Fonds zur Förderung der wissenschaftlichen Forschung, I 4945-N) and the ANR (Agence Nationale de la Recherche, ANR-20-CE91-0006).

Research topics

Many numbertheoretic sequences are per se deterministic but resemble much of the overall behaviour of a random sequence. One important example is the Möbius function. In this context we are interested in studying the independence between the Möbius function and various deterministic functions such as functions that are produced by a dynamical system of zero entropy or by a simple algorithm based on the binary digital representation. Informally, the difficulty of this independence problem reflects the difficulty of the transition from the digital representation of an integer to its multiplicative representation as a product of prime factors. This field of questions is the source of many important open problems in mathematics and computer science. In particular, we mention the construction of normal numbers, the analysis of pseudo-random and complexity measures, and the search for optimal discrepancy estimates for digitally based sequences or other quasi-random sequences which are some of the major lines of research in this joint project.

Members

The Austrian-French Consortium consists of 16 researchers and is based in Graz, Vienna, Bordeaux, Calais, Marseille, Nancy and St Etienne.

Aistleitner Christoph (Technische Universität Graz)
Dartyge Cécile (Université de Lorraine)
Deshouillers Jean-Marc (Institut polytechnique de Bordeaux)
Drappeau Sary (Université d'Aix-Marseille)
Drmota Michael (Technische Universität Wien)
Elsholtz Christian (Technische Universität Graz, Austrian Coordinator)
Grabner Peter (Technische Universität Graz)
Martin Bruno (Université du Littoral)
Müllner, Clemens (Technische Universität Wien)
Ramaré Olivier (Université d'Aix-Marseille)
Rivat Joël (Université d'Aix-Marseille)
Robert Olivier (Université Jean Monnet, Lyon, St Etienne)
Spiegelhofer Lukas (Technische Universität Wien)
Stoll Thomas (Université de Lorraine, French coordinator)
Tenenbaum Gérald (Université de Lorraine)
Tichy Robert (Technische Universität Graz)

Postdoctoral researchers:

Pierre-Yves Bienvenu (Graz)

Kübra Benli (Nancy)

Andrei Shubin (Vienna)

Doctoral students:

Vincent Gozé (Calais-Littoral)

Events

Workshop ArithRand 22 Workshp ArithRand 22
Partial funding of Workshp Aaa7 Graz 2024
Talks by visitors (or online)
Arithrand-related talks at Ernest seminar (Luminy, Marseille, FR)
2021-12-07: Joni Teräväinen, On a hybrid of the Hardy-Littlewood and Chowla conjectures
2021-06-08: Gregory Debruyne, Malliavin-type remainders for Beurling generalized prime number systems
2021-05-11: Johann Verwee, Théorèmes d'Erdős-Wintner effectifs
2021-04-13: Pierre-Adrien Tahay, Corrélations discrètes d’ordre 2 de suites généralisées de Rudin-Shapiro par une approche combinatoire
2020-12-08: Youness Lamzouri, La répartition du maximum des sommes partielles de sommes d'exponentielles

Seminars with links to ArithRand ("Metz-Nancy Number Theory Seminar" at IECL, Nancy)
9/12/2021, Journée Scientifique FCH "Pseudorandomness, cryptography and number theory" (IECL/LORIA)
2/12/2021 Benli Kübra (IECL), Changes in digits of primes
18/11/2021 Sébastien Darses (Aix-Marseille Université), On probabilistic generalizations of the Nyman-Beurling criterion for the Zeta function
21/10/2021 Manfred Madritsch (IECL), Construction d'un nombre normal tel que son inverse soit également normal
30/09/2021 Yann Bugeaud, Approximation rationnelle des nombres sturmiens
20/05/2021 (online) Kübra Benli, Small prime power residues modulo p
15/04/2021 (online) Gérald Tenenbaum (IECL), Répartition des fonctions multiplicatives dans les progressions arithmétiques de grands modules et applications
08/04/2021, (online) Paul Pollack (University of Georgia), Multiplicative orders mod p
01/04/2021 (online) Sarah Peluse (IAS/Princeton), Modular zeros in the character table of the symmetric group
11/03/2021 (online) Alessandro Languasco, On computing L'/L(1,chi) and related problems
18/02/2021 (online) Brad Rodgers, The distribution of random polynomials with multiplicative coefficients
07/01/2021 (online) Marc Munsch, Comportement aléatoire local des suites réelles: résultats métriques, énergie additive et inégalités diophantiennes
10/12/2020 (online) Johann Verwee, Théorèmes d'Erdös-Wintner effectifs
19/11/2020 (online) Amri Myriam, Sur la répartition jointe de la représentation d'Ostrowski dans les classes de résidus
12/11/2020 (online) Jakub Konieczny, Automatic multiplicative sequences
15/10/2020 Shuo Li, On the classification of completely multiplicative automatic sequences

Talks at the Ernest seminar in Marseille :
2022-12-01, Jared D. Lichtman, "A proof of the Erdős primitive set conjecture"
2022-10-18, Michael Drmota, "Primes as sums of Fibonacci numbers" >li>2022-10-04, Olivier Ramaré, "A Stronger Model for Peg Solitaire"
2022-06-14, Cécile Dartyge, "Valeurs polynomiales quartiques avec un grand facteur premier : les cas diédraux et cycliques"
2022-05-10, Andreas Weingartner, "A general sieve problem"
2022-04-05, Nicole Raulf, "Sur le comportement d'un produit de fonctions L"
2022-03-01, Kübra Benli, "Small prime 𝑘-th power residues modulo 𝑝"
2022-02-01, Corentin Darreye, "Oscillations dans la suite des coefficients d'une forme modulaire"
2022-01-18, Jakub Konieczny, "Finitely-valued generalised polynomials"
2023-11-07, Cathy Swaenepoel, Nombres premiers réversibles
2023-09-19, Marco Aymone, Convolution of periodic multiplicative functions and the divisor problem
2023-06-20, Jungwon Lee, Dynamics of Ostrowski skew-product: Limit laws and Hausdorff dimensions
2023-06-13, Régis de la Bretèche, Sommes friables de fonctions arithmétiques
2023-06-06, Thomas Stoll, Complexité d'ordre maximal des suites automatiques et morphiques
2023-04-18, Gopal Maiti, Extreme values of quadratic Dirichlet L-functions over function fields
2023-04-11, Marco Aymone, Multiplicative functions with small partial sums
2023-03-21, Rachid Caich, Majorations presque sûres de sommes de fonctions multiplicatives aléatoires
Reading seminar at IECL Nancy, Primes as sums of Fibonacci numbers (Fall 2021-Spring 2022)
---Seminars related to ArithRand on Nancy
Questions d'équirépartition de sommes exponentielles indexées par un sous-groupe, 27 janvier 2022, Théo Untrau (IMB, Bordeaux)
Ensembles de formes linéaires de complexité maximale, 3 février 2022, Michel Waldschmidt (Sorbonne Université)
2022-03-03, Fernando Xuancheng Shao (University of Kentucky), Gowers uniformity of thin subsets of primes
2022-04-07, Cécile Dartyge (IECL), Valeurs polynomiales quartiques avec un grand facteur premier : les cas diédraux et cycliques
2022-04-28, Jonathan Bober (Université de Bristol), The distribution of character sums
2022-05-05, Andreas Weingartner (Southern Utah University, États-Unis), A general sieve problem
2022-05-12, Lola Thompson (Université de Utrecht), Summing mu(n): an even faster elementary algorithm
2022-06-22, Frederik Broucke (Ghent University), Well-behaved Beurling number systems
2022-06-22, Gregory Debruyne (Ghent University), Optimality for Tauberian theorems
2022-06-23, Shalom Eliahou (Université du Littoral Côte d'Opale), Quelques problèmes ouverts sur des familles de suites binaires
2022-06-23, Igor Shparlinski (University of New South Wales), Sums of Kloosterman sums with multiplicative coefficients
2022-11-10, Olivier Robert (Université JeanMonnet, Saint Étienne; Institut Camille Jordan), Points rationnels sur une intersection de formes diagonales
2022-12-01, Paul Péringuey (IECL), Une généralisation de la conjecture d'Artin parmi les presque premiers
2022-12-08, Pierre Popoli (IECL), Suites automatiques et morphiques de grande complexité le long des sous-suites
2022-12-15, Emilie Charlier (université de Liège), Non-canonical Bertrand numeration systems
2023-03-09, Rachid Caich (université de Paris, IMJ), Majorations presque sûres de sommes de fonctions multiplicatives aléatoires
2023-03-16, Cathy Swaenepoel (université de Paris, IMJ), Nombres premiers et carrés avec des chiffres préassignés
2023-06-15, Jacques Benatar (université de Helsinki), Polynômes à coefficients multiplicatifs
2023-06-22, Jared Lichtman (University of Oxford), A proof of the Erdős primitive set conjecture
2023-11-23, Julia Stadlmann (Université d'Oxford), Primes in arithmetic progressions to smooth moduli
2023-12-21, Cathy Swaenepoel (Institut de Mathématiques de Jussieu), Nombres premiers réversibles

Guests (selection)

to come

For your upcoming or to be published papers, please include : "This paper was supported by the joint FWF-ANR project Arithrand: FWF: I 4945-N and ANR-20-CE91-0006."

Publications-Preprints - in preparation (explicitely mentioning ArithRand)

C. Aistleitner, B. Borda: Quantum invariants of hyperbolic knots and extreme values of trigonometric products. Math. Z. 302 (2022), no. 2, 759–782.
C. Aistleitner, D. El-Baz, M. Munsch: A pair correlation problem, and counting lattice points with the zeta function. GAFA 31 (2021), no. 3, 483--512
C. Aistleitner, S. Baker, N. Technau, N. Yesha: Gap statistics and higher correlations for geometric progressions modulo one. Math. Ann. 385 (2023), no. 1-2, 845–861. arxiv:2010.10355
C. Aistleitner, N. Gantert, Z. Kabluchko, J. Prochno, K. Ramanan: Large Deviation Principles for Lacunary Sums. Trans. Amer. Math. Soc. 376 (2023), no. 1, 507–553. Preprint, arxiv:2012.05281
C. Aistleitner, B. Borda: Maximizing Sudler products via Ostrowski expansions and cotangent sums. Algebra Number Theory 17 (2023), no. 3, 667–717. arXiv:2104.01379
C. Aistleitner, D. El-Baz, M. Munsch: Difference sets and the metric theory of small gaps. Preprint, Int. Math. Res. Not. IMRN 2023, no. 5, 3848–3884. arXiv:2108.02227
C. Aistleitner, B. Borda: A conjecture of Zagier and the value distribution of quantum modular forms. JEMS, to appear, arXiv:2110.07407
Aloui, K.; Jamet, D., Kaneko, H., Kopecki, S., Popoli, P; Stoll, T. On the binary digits of n and n^2, (2022), Theoretical Computer Science 939 (2022), 119--139. https://arxiv.org/abs/2203.05451, https://doi.org/10.1016/j.tcs.2022.10.018
Aymone, M; Maiti, G.; Ramaré, O.; Srivastav, P. On the Convolution of Periodic Multiplicative functions, 2023; (Submitted); https://arxiv.org/abs/2305.06260
M. Balazard, B. Martin, Démonstration d’une conjecture de Kruyswijk et Meijer sur le plus petit dénominateur des nombres rationnels d’un intervalle, to appear in Bull. Sci. Math. https://doi.org/10.1016/j.bulsci.2023.103305, arXiv:2303.01303v1, hal-04010689
G. Barat, B. Martin, C. Mauduit, J. Rivat, Fonctions additives en base de Cantor le long des nombres premiers, preprint.
V. Becher, A. Marchionna, G. Tenenbaum, On simply normal numbers with digit dependencies, Mathematika 69, no. 4 (2023), 988-991.
K. Benli, G. Cesana, C. Dartyge, C. Dombrowsky, L. Thompson, Sum of proper divisors with missing digits, to appear in WiNE-4 Proceedings, preprint available at https://arxiv.org/abs/2307.12859
K. Benli, E. Elma, N. Ng, A discrete mean value of the Riemann zeta function, submitted, preprint available at https://arxiv.org/abs/2311.13554 [arxiv.org]
Benli, K.; Stoll, T. Subword complexity of the Fibonacci-Thue-Morse sequence along polynomials, in preparation.
Bettin, S.; Drappeau, S. Two arithmetic applications of perturbations of composition operators. J. Anal. Math. 144 (2021), 335--349. DOI: 10.1007/s11854-021-0184-1. arXiv:2002.11417. hal-02493843v1.
Bettin, S.; Drappeau, S. Effective estimation of some oscillatory integrals related to infinitely divisible distributions. Ramanujan J. 57 (2022) 849--861. DOI: 10.1007/s11139-020-00362-y. arXiv: 2010.15494. HAL:hal-02998544v1.
Bettin, S.; Drappeau, S. Modularity and value distribution of quantum invariants of hyperbolic knots. Math. Ann. 382 (2022) no. 3-4, 1631--1679. DOI: 10.1007/s00208-021-02288-2. arXiv:1905.02045. HAL: hal-02998581v1.
Bettin, S.; Drappeau, S. Limit laws for rational continued fractions and value distribution of quantum modular forms. Proc. London Math. Soc. 125 (2022), no 6, 1377--1425. DOI: 10.1112/plms.12485. arXiv:1903.00457. HAL: hal-02998562v1.
Bettin, S.; Drappeau, S. On quantum modular forms of non-zero weights, submitted. arXiv:2210.07854.
Bienvenu, P.-Y. and Geroldinger, A., On algebraic properties of power monoids of numerical monoids, Isr. J. Math., to appear.
Bienvenu, P.-Y, Metric decomposability theorems on sets of integers, Bull. London Math Soc., https://doi.org/10.1112/blms.12886
S. Boyer, O. Robert, Rational points on an intersection of diagonal forms, Acta Arith. 203 (2022), no. 2, 165-194
La Bretèche, R.; Dress, F.; Tenenbaum, G., Remarques sur une somme liée à la fonction de Möbius, Mathematika 66, no. 2 (2020), 416--421.
La Bretèche, R.; Munsch, M.; Tenenbaum, G., Small Gál sums and applications, J. London Math. Soc. 103}(2021), 336--352.
La Bretèche, R. Tenenbaum, G., Remarks on the Selberg--Delange method, Acta Arith. 200.4 (2021), 349-369.
La Bretèche, R. Tenenbaum, G., On strong and almost sure local limit theorems for a probabilistic model of the Dickman distribution, Lith. Math. J. 61, n°3 (2021), 301-311.
R. de la Bretèche, G. Tenenbaum, On the gap distribution of prime factors, Proc. Amer. Math. Soc. 151, \no. 8 (2023), 3245–3251.
R. de la Bretèche, G. Tenenbaum, Friable averages of oscillating multiplicative functions, in: H.~Maier, J. Steuding, R. Steuding (eds.), Number Theory in memory of Eduard Wirsing, 43-79, Springer, 2023.
R. de la Bretèche, G. Tenenbaum, Two upper bounds for the Erd\H os--Hooley Delta-function, Sci. China Math. 66, no. 12 (2023), 2683–2692.
R. de la Bretèche, G. Tenenbaum, Note on a conjecture of Hildebrand regarding friable integers, Acta Arith. 208 (2023), 279-283.
R. de la Bretèche, G. Tenenbaum, Friable averages of complex arithmetic functions, prépublication.
J. Brüdern, O. Robert, On the sum of two powered numbers, to appear in Acta Arithmetica
F. Chamizo, B. Martin, The convergence of certain Diophantine series, J. Number Theory, 229 (2021), 179-198. https://doi.org/10.1016/j.jnt.2021.04.022 hal-04154176v1
F. Chamizo, B. Martin, The approximate functional equation of some Diophantine series, Monatsh. Math., 202 (2023), 41-52. https://doi.org/10.1007/s00605-023-01859-6 hal-04154260v1
Chamizo, F ; Martin, B. The approximate functional equation of some Diophantine series, submitted.
B. Cook, K. Hughes, Z. Kun Li, A. Mudgal, O. Robert, P-L Yung - A decoupling interpretation of an old argument for Vinogradov's Mean Value Theorem, to appear in Mathematika
Darbar, P.; Maiti, G. Large values of quadratic Dirichlet L-functions over monic irreducible polynomial in $\mathbb{F}_q [t]$; To be appear in Proceedings of the American Mathematical Society, 2023; https://arxiv.org/abs/2311.10419
Dartyge, C; Feutrie, D.; Tenenbaum, G., Entiers ultrafriables en progressions arithmétiques, Quart. J. Math. (Oxford) 73 (2022), 149-74.
Dartyge, C.; Maynard, J.; On the largest prime factor of quartic polynomial values: the cyclic and dihedral case, arXiv:2212.03381.
C. Dartyge, B. Martin, J. Rivat, I. Shparlinski, C. Swaenepoel, Reversible primes, preprint. arXiv:2309.11380v1
Ddamulira, M., Luca, F. & Tichy, R., On the Shorey–Tijdeman Diophantine equation involving terms of Lucas sequences; Indagationes Mathematicae. 33, 2, (2022), p. 314--321.
Debruyne, G.; Tenenbaum, G., The saddle point method for general partitions, Indag. Math. 31 (2020), 728-738.
Jean-Marc Deshouillers, Michael Drmota, Clemens Müllner, Andrei Shubin, Lukas Spiegelhofer; Synchronizing automatic sequences along Piatetski-Shapiro sequences; Israel J. Math., to appear, arXiv:2211.01422
Jean-Marc Deshouillers, Michael Drmota, Clemens Müllner; Coprimality of consecutive elements in a Piatetski-Shapiro sequence; in: Number Theory in Memory of Eduard Wirsing, Springer, to appear.
Drappeau, S.; Hanna, G. The Thue–Morse and Rudin–Shapiro sequences at primes in principal number fields. Acta Math. Hung. 162 (2020), 130--186. Zbl 1398.11121; MR4169024. DOI: 10.1007/s10474-020-01030-9. arXiv:2001.07017. HAL:hal-02493862v1.
Drappeau, S.; Fiorilli, D. The first moment of primes in arithmetic progressions: beyond the Siegel-Walfisz range. Trans. London Math. Soc. 8 (2021), no 1, 174--185. DOI: 10.1112/tlm3.12030. arXiv: 2003.02201. HAL:hal-02567736v1.
Drappeau, S.; Pratt, K.; Radziwiłł, M. One-level density estimates for Dirichlet L-functions with extended support. Algebra Number Theory, 17 (2023), no. 4, 805--830. arXiv:2002.11968. HAL: hal-02493847v1.
Acharya, R.; Drappeau, S.; Ganguly, S.; Ramaré, O., A modular analogue of a problem of Vinogradov. Ramanujan J., 62 (2023), no. 2, 365--382. hal-04052941, arXiv:2208.14786, DOI:https://dx.doi.org/10.1007/s11139-022-00688-9
Drappeau, S.; Nordentoft, A., Central values of additive twists of Maaß forms L-functions. submitted, arXiv:2208.14346, hal-04052946.
M. Drmota, M. Lemańczyk, C. Müllner, J. Rivat; Some recent developments on the Sarnak conjecture, in: "Panoramas et Syntheses", Soc. Math. de France, to appear.
Michael Drmota, Christian Mauduit, Joël Rivat, Lukas Spiegelhofer: Möbius orthogonality of sequences with maximal entropy. Journal d'Analyse Mathématique 146 (2022), 531--548; arxiv:2001.07898
Michael Drmota, Clemens Müllner, Lukas Spiegelhofer; Primes as sums of Fibonacci numbers; Memoirs of the American Mathematical Society, to appear; arXiv:2109.04068
Elsholtz, C.; Planitzer, S., Sums of four and more unit fractions and approximate parametrizations. Bull. Lond. Math. Soc. 53 (2021), no. 3, 695--709.
Elsholtz, C. Fermat's last theorem implies Euclid's infinitude of primes. Amer. Math. Monthly 128 (2021), no. 3, 250--257.
Elsholtz, C.; Klahn, B.; Technau, M.; On polynomials with roots modulo almost all primes Acta Arithmetica 205 (2022), 251-263. DOI: 10.4064/aa220407-9-7
Rainer Dietmann, Christian Elsholtz, Alexander Kalmynin, Sergei Konyagin, James Maynard, Longer gaps between values of binary quadratic forms, Int. Math. Res. Not. IMRN 2023, no. 12, 10313–10349. https://doi.org/10.1093/imrn/rnac130
Elsholtz, C.; Lipnik, G.; Exponentially Larger Affine and Projective Caps, Mathematika 69 (2023), no. 1, 232–249. https://doi.org/10.1112/mtk.12173
Elsholtz, C.; Klahn, B.; Lipnik, G.; Large subsets of (Z_m)^n without arithmetic progressions, Des. Codes Cryptogr. 91 (2023), no. 4, 1443–1452. https://doi.org/10.1007/s10623-022-01145-w
Elsholtz, C.; Heuberger, C; Krenn, D. Algorithmic counting of nonequivalent compact Huffman codes, Applicable Algebra in Engineering, Communication and Computing (2023) https://doi.org/10.1007/s00200-022-00593-0
Fouvry, É.; Tenenbaum, G., Multiplicative functions in large arithmetic progressions and applications, Trans. Amer. Math. Soc. 75, no. 1 (2022), 245-299.
S. Heintze, R. Tichy, I. Vukusic, V. Ziegler. On the Diophantine equation $U_n-b^m=c$, Mathematics of Computation 92, 344 (2003), 2825-2859.
Jamet, D.; Popoli, P.; Stoll, T. Maximum order complexity of the sum of digits function in Zeckendorf base and polynomial subsequences. Cryptography and Communications 13 (2021), 791--814. https://doi.org/10.1007/s12095-021-00507-w, https://arxiv.org/abs/2106.09959
Kaneko, H.; Stoll T. Products of integers with few nonzero digits. Uniform Distribution Theory Unif. Distrib. Theory 17 (2022), no. 1, 11--28, https://doi.org/10.2478/udt-2022-0006, http://arxiv.org/abs/2112.03077
Klahn, B., Technau, M. Galois groups of n0 + n1 X + … + n6 X^6 Int. J. Number Theory, 2023, 19, 2443-2450.
Jakub Konieczny; Clemens Müllner. Arithmetical subword complexity of automatic sequences. submitted. arXiv: 2309.03180
Jakub Konieczny; Clemens Müllner. Bracket words along Hardy field sequences. to appear in Ergodic Theory and Dynamical Systems. arXiv: 2302.09626
Elżbieta Krawczyk, Clemens Müllner, Automaticity of uniformly recurrent substitutive sequences, https://arxiv.org/abs/2111.13134
Dijana Kreso, Joel Rivat, Robert Tichy (editors). Diophantine Problems: Determinism, Randomness and Applications
G.F. Lipnik; M. Madritsch; R. Tichy, A Central Limit Theorem for Integer Partitions into Small Powers, Monatshefte Math., to appear.
Marcovici, I.; Tahay, P.-A.; Stoll, T. Discrete correlations of order 2 of generalised Golay-Shapiro sequences: a combinatorial approach. Integers 21 (2021), A45, 21pp. http://math.colgate.edu/~integers/vol21.html, https://arxiv.org/abs/2006.13162
B. Martin, G. Tenenbaum, J. Wetzer, On the friable mean-value of the Erdős-Hooley Delta function, preprint. arXiv:2307.05530
J. Di Mauro, G. Millerioux, M. Minier, T. Stoll : Provable randomness over lightweight permutations, submitted
Paolo Minelli, Athanasios Sourmelidis & Marc Technau, Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums, Math. Ann. 2023, 387, 291-320. https://doi.org/10.1007/s00208-022-02452-2
Minelli, P.; Sourmelidis, A., Technau, M. On restricted averages of Dedekind sums Int. Math. Res. Not. IMRN.
M. Radziwiłł, A. Shubin, "Poissonian pair correlation for \alpha n^{\theta} mod 1", IMRN, to appear https://doi.org/10.1093/imrn/rnad289, https://arxiv.org/abs/2304.04621
O. Ramare, Notes on restriction theory in the primes, arXiv:2109.10180
A. Shubin, Möbius orthogonality of Thue-Morse sequence along Piatetski-Shapiro numbers, Studia Math. 273 (2023), no. 3, 201-238, https://arxiv.org/abs/2207.11840
Spiegelhofer, L., Gaps in the Thue--Morse word. J. Aust. Math. Soc. 114, no. 1 (2023), 110-144, https://www.doi.org/10.1017/S1446788721000380, arXiv:2102.01018v2
Spiegelhofer, L., Collisions of digit sums in bases 2 and 3. Israel J. Math., to appear. arXiv:2105.11173v2
Spiegelhofer, L., Thue--Morse along the sequence of cubes, https://arxiv.org/abs/2308.09498
Bartosz Sobolewski and Lukas Spiegelhofer, Block occurrences in the binary expansion, https://arxiv.org/abs/2309.00142
Technau, M. Remark on the Farey fraction spin chain Proc. Amer. Math. Soc., 2024, 152, 63-69
Tenenbaum, G., A note on the normal largest gap between prime factors, J. Théor. Nombres Bordeaux 31, no. 3 (2019), 747-749.
Tenenbaum, G.; Verwee, J., Effective Erd\H os--Wintner theorems, Proc. Steklov Inst. Math. 314 (2021), 275--289.
Tenenbaum, G.; Weingartner, A., An Erd\H{o}s-Kac theorem for integers with dense divisors, preprint.
Tichy, R., Vukusic, I., Yang, D. & Ziegler, V., Integers representable as differences of linear recurrence sequences; Research in Number Theory 7, (2021), 24.

Talks

Talks on "On algebraic properties of power monoids of numerical monoids":
June 2022, Hebei Open seminar (online/invited)
November 2022, Mississippi Number Theory Seminar (online)
December 2022, Uni Graz Algebra and Number Theory Seminar (online)
Talks on "Metric decomposability theorems on sets of integers" July 2022, Arith Rand workshop (in person)
Algebra and Number Theory Seminar, University College Dublin, Februar 2023.
by Cecile Dartyge
27/09/2021 Rencontres de théorie analytique et élémentaire des nombres (Paris), "Valeurs polynomiales quartiques avec un grand facteur premier, les cas diédraux et cycliques".
17 mars 2022, séminaire de théorie des nombres de Grenoble, "Valeurs polynomiales quartiques avec un grand facteur premier, les cas diédraux et cycliques".
31 mars 2022 Séminaire de théorie des nombres de Nancy-Metz, "Répartition des nombres premiers dans des suites d'entiers".
1er avril 2022 Séminaire Bourbaki du vendredi, "Répartition des nombres premiers dans des suites d'entiers".
21 juin 2022 Séminaire ADA à Calais, "Valeurs polynomiales quartiques avec un grand facteur premier, les cas diédraux et cycliques".
4--8 Juillet 2022, Number Theory Conference 2022 à Debrecen (Hongrie), conférence en l'honneur de K\'alm\'an Gy\H ory, J\'anos Pintz et Andr\'as S\'ark\''ozy. (Exposé annulé en raison du COVID).
25 novembre 2022, Séminaire de théorie des nombres de Bordeaux, "Valeurs polynomiales quartiques avec un grand facteur premier, les cas diédraux et cycliques".
6--12 novembre 2022, Workshop "Analytic Number Thoery", Oberwolfach, Allemagne, On the largest prime factor of quartic polynomial^Mvalues: the cyclic and dihedral cases
5--9 septembre 2022, A celebration of analytic number theory, a conference in honor of Andrew Granville, CRM Montréal, Canada. On the largest prime factor of quartic polynomial values: the cyclic and dihedral cases
8 décembre 2022, Xi'an Jiatong University (Chine), On the largest prime factor of quartic polynomial values: the cyclic and dihedral cases (exposé en ligne).
19 janvier 2023, Number Theory Web Seminar, On the largest prime factor of quartic polynomial^Mvalu\ es: the cyclic and dihedral cases (exposé en ligne).
13 mars 2023, Number Theory Seminar, Warwick University, (Grande Bretagne)
4--6 mai 2023, 7th Minisymposium of the Roman number theory association, (Italie)

by Sary Drappeau
"Modularity of the q-Pochhammer symbol and application", 2020-11-27, CIRM Conference "Diophantine Problems, Determinism and Randomness".
"The distribution of the Estermann function and other quantum modular forms", 2021-03-01, Mittag-Leffler semester on Number Theory.
"Fractions continues et lois limites pour quelques valeurs de fonctions L", 2021-05-21, Séminaire de Dynamique de l'IMJ-PRG.
"Continued fractions and limit laws for values of L-functions", 2021-05-28, N-Cube days.
"Shifted convolutions, arithmetic progressions, exponential sums", 2021-06-28 to 2021-07-02, 4 talks at the Paris Summer School in Analytic Number
"Quantum modularity for central values of additively twisted Maass L function", 2022-05-31, Genova-Graz Number Theory Workshop, Genova, Italy
"Quantum modularity of additive twists of Maass L values", 2022-09-06, Celebrating Analytic Number Theory, conference in honour of Andrew Granville, Montreal, Québec, Canada
"The central limit theorem for values of the Estermann function", 2022-09-28, Stanford Number Theory Students online seminar
"Formes modulaires quantiques de poids non nul", 2022-10-03, Rencontres de Théorie Analytique et Élémentaire des Nombres, IHP Paris, France
"Modularité quantique pour les tordues additives de fonctions L des formes de Maass", 2022-11-15, Séminaire de
Théorie des Nombres de Clermont-Ferrand, France
Bordeaux, France (seminar, invited) 2023-09-29. Quantum modular forms of non-zero weight.
ISI, Kolkata, India (seminar, invited) 2023-02-01. Quantum modular forms of non-zero weight.
ISI, Kolkata, India (conference, invited) 2023-02-08. Quantum modularity for central values of additively twisted Maass L-functions
IHP, Paris, France (seminar, invited) 2022-10-03. Formes modulaires « quantiques » de poids non nul
Genova, Italy (workshop, invited) 2022-05-31. Quantum modularity for central values of additively twisted Maass L-functions
Montreal, Canada (conference, invited) 2022-09-06. Quantum modularity for central values of additively twisted Maass L-functions
MPI, Bonn, Germany (workshop, invited) 2023-04-25. Quantum modularity for central values of additively twisted Maass L-functions
CIRM, Marseille, France (workshop, invited), 2023-09-25. Quantum modular forms of non-zero weight.

by Michael Drmota
online, contributed, (Logarithmic) Densities for Automatic Sequences along Primes and Squares AG Diskrete Mathematik, TU Wien, March 16, 2021
online, invited, (Logarithmic) Densities for Automatic Sequences along Primes and Squares One World Numeration Seminar, March 30, 2021
in person, contributed, Primes as Sums of Fibonacci Numbers AG Diskrete Mathematik, TU Wien, October 12, 2021
in person, contributed, Subsequences of Automatic Sequences and Uniform Distribution, SFB-Meeting Traunkirchen, January 14, 2022.
in person, invited, Primes as Sums of Fibonacci Numbers, Univ. Tours, Seminar, March 17, 2022.
in person, invited, Primes as Sums of Fibonacci Numbers I., ArithRand 2022, TU Graz, July 2, 2022.
online, constributed, The Sarnak conjecture and related questions on the Fibonacci-Thue-Morse sequence, Russian-Austrian Joint Meeting, July 12, 2022.
in person, invited, Primes as Sums of Fibonacci Numbers, Univ. Aix-Marseille, Marseille, Seminar, October 10, 2022.
online, invited, Moebius orthogonalily: a classical and modern topic in number theory, Univ. Xiamen, China, October 27, 2022.

by Christian Elsholtz
Large sets in (Z_m)^n without progressions 7 Sep 2020 - 11 Sep 2020, Cirm (Luminy, online)
Improved cap constructions, and sets without arithmetic progressions, Conference: Diophantine Problems: Determinism, Randomness, Applications 23 Nov 2020 - 27 Nov 2020, CIRM Luminy (online)
Sums of unit fractions, March 18, 2021, Karl Franzens University Graz
Improved cap constructions, and sets without arithmetic progressions, March 25, 2021, Karl Franzens University Graz
Fermat's Last Theorem implies Euclid's infinitude of the primes, Combinatorial and additive number theory, CANT 2021 (New York, online), 24 Mai 2020 - 28 May 2021
Improved cap constructions, and sets without arithmetic progressions, June 3, 2021, Laboratoire Analyse, Géométrie et Applications, Paris, Frankreich, invited.
Arithmetic progressions in arithmetic sets, June 11, 2021, Salzburg-Debrecen-Graz seminar, invited.
Fermat's last theorem implies Euclid's infinitude of primes, Jun 24, 2021. Karl-Franzens-Universität Graz.
Improved cap constructions in affine and projective spaces, 29.9.2021, DMV-ÖMG Tagung, Passau (contributed, virtual)
^ Lower bound constructions for progression-free sets and caps in affine and projective spaces. Number theory seminar, Alfred Renyi-Institute, (invited, virtual)
Lower bound constructions for progression-free sets and caps in affine and projective spaces. COmbinatorial Number Theory And Connected Topics (CONTACT - I), India, (invited speaker, virtual)
Longer gaps between values of binary quadratic forms, Event title Number Theory Conference 2022: In honour of Professors Kálmán Győry, János Pintz and András Sárközy, Debrecen, July 2022.
Constructing large sets avoiding certain structure, Graz, Discrete Mathematics Colloquium.
Unendlich viele Beweise für unendlich viele Primzahlen - Variationen zum Satz von Euklid P.H. Ludwigsburg (Germany) 24.5.2023
Improving high dimensional constructions, for caps and progression-free sets, by studying medium dimensions, Meeting of the Austrian Mathematical Society, Graz, 18.9.2023.
Gaps between values of binary quadratic forms, seminar of the Doctoral School, Graz, 1.12.2023.
Lower bounds for progression free sets and caps in F_p^n, ISTA, (Browning group, Working Seminar), 13.12.2023.

by G. Maiti
Convolution of periodic multiplicative functions and the divisor problem, Rencontres de théorie analytique et élémentaire des nombres, Institut Henri Poincaré, Paris, 20 November, 2023.
Convolution of periodic multiplicative functions and the divisor problem, Arithmetic and Number Theory Seminar, Paul Painlevé Laboratory, Université de Lille, 23 November, 2023
Simultaneous non-vanishing of quadratic Dirichlet $L$-functions and twists of Hecke $L$-functions, Number Theory Seminar, Department of Mathematics, University of Genova, Italy, 23 May, 2023.
Extreme values of quadratic Dirichlet L-functions over function fields, Séminaire Ernest, Institut de Mathématiques de Marseille, Marseille, 14 March, 2023.

by Bruno Martin
invited online talk in the Conference "Diophantine Problems, Determinism and Randomness" in Cirm, 24th november 2020. Title " Some interactions between number theory and multifractal analysis".
Transformation de Gauss, équations fonctionnelles et comportement multifractal, Conférence de deux jours pour les 60 ans de Stéphane Jaffard, Institut Henri Poincaré, Paris, 8 juin 2023 (invited, in person)

by Clemens Müllner
Multiplicative automatic sequences, Open University Dynamical Systems seminar of 2021, 13. January 2021 (invited)
Multiplicative automatic sequences, One World Numeration Seminar 9. February 2021 (contributed)
Substitution dynamical systems in the context of Sarnak's conjecture Seminar: AG Ergodic Theory (University of Vienna) am 10.11.2022 (in person).

by O. Ramare
O. Ramaré, 4 octobre 2021, Séminaire de Théorie des Nombres de Paris, Polynomes trigonom'etriques arithm'etiques aux points de petites hauteurs, in person
6-17 December 2021, Density Estimates and Additive Combinatorics, brainstorming session with four participants, with the support of ArithRand https://www.i2m.univ-amu.fr/events/density-estimates-and-additive-combinatorics/

by Olivier Robert
AGNT Seminar, Chalmers, June 2nd 2022 : Rational points on an intersection of diagonal forms
Séminaire de combinatoire et de théorie des nombres (Lyon), October 4th 2022, Points rationnels sur une intersection de formes diagonales
Séminaire de Théorie des Nombres (Nancy) : November 10th 2022 : Points rationnels sur une intersection de formes diagonales
Göttingen April 17th 2023 (invited to the Seminar): Rational points on an intersection of diagonal forms
Séminaire de combinatoire et de théorie des nombres (Lyon), October 17th 2023, Sur une généralisation des puissances d'un entier ("powered numbers"). Application à un problème additif.

by Joel Rivat
"Pseudo-random properties of sums and products", Debrecen 2022.
by Andrei Shubin
in person, contributed, Primes in subsets and exponential sums, AG Diskrete Mathematik, TU Wien, Nov 9, 2021
01/07/2022, in person, contributed, Automatic sequences along Piatetski-Shapiro sequences, ArithRand 22, Graz, 1-2 July, 2022
22/08/2022, in person, contributed, Automatic sequences along Piatetski-Shapiro numbers, ELAZ, A conference on elementary and analytic number theory, August 2022
25/01/2023, in person, contributed, On pair correlations of monomial sequences, Browning group working seminar, IST Austria, January 2023

by Lukas Spiegelhofer
The level of distribution of the Thue--Morse sequence, Rencontres de th\'eorie analytique et \'el\'ementaire des nombres, Paris, France, in person, invited, 21 March 2022
Collisions of digit sums in different bases, Rencontres de th\'eorie analytique et \'el\'ementaire des nombres, Paris, France, in person, invited, 21 March 2022
Primes as sums of Fibonacci numbers, ArithRand 2022, TU Graz, Austria, in person, contributed, 2 July 2022
Primes as sums of Fibonacci numbers, One World Numeration Seminar, contributed online talk, 11 Oct 2022
Thue--Morse along the sequence of cubes, ÖMG Tagung in Graz, Austria, September 2023.
Subsequences of digitally defined functions, IMath Webinar Series of the University of the Philippines Diliman, November 2023
The simplest 2-regular sequences, JKU Linz, Austria, December 2023

by Thomas Stoll
On difference matrices and generalised Rudin-Shapiro sequences, Plenary talk, online, 7th International Conference on Uniform Distribution Theory (UDT2021), 24-02-2021.
online, invited, The sum of digits of polynomials, special lecture, Shandong University at Weihai (Chine), 16/1/23
06/06/2023 : T. Stoll, Complexité d'ordre maximal des suites automatiques et morphiques, Marseille, Séminaire Ernest
20/11/2023 : T. Stoll, Lemme de Hensel pour les fonctions continues p-adiques, Rencontres de théorie analytique et élémentaire des nombres, IHP Paris
25/01/2024 : T. Stoll, Lemme de Hensel pour les fonctions continues p-adiques, Séminaire de Théorie des Nombres de Nancy-Metz
by G. Tenenbaum
Number Theory Web Seminar, 10 novembre 2020. Diophantine Problems, Determinism and Randomness, CIRM, Luminy, 23-27 novembre 2020.
Analytic & combinatorial number theory in honour of R. Balasubramanian, IMSc, Chennai, 16 march, 2021, (online).
Sommes de Gál et applications, invited, Colloquium université de Reims, 25/1/2022
Friable averages, a survey, invited, ELAZ 2022, a conference on Elementary and Analytic Number Theory, Poznań, 24/8/2022.

by R. Tichy
QMC methods in finance and insurance, University Lausanne, 24.04.2023.

by V. Gozé
Poster presentation in Congress for Young Researchers in Mathematics and its Applications 2022 (22/09/22) in Calais: "The prime number theorem".
Talk on "Average order of arithmetic functions and the prime number theorem" in the PhD student seminar in Calais (04/05/23).
Poster presentation in "Journées des doctorants du pôle MTE" (20/06/23, intended for a non-expert audience) in Calais.