Reminder

In all DK related publications, it is required to acknowledge support of the FWF. The following naming convention must be used in all cases:

    Austrian Science Fund (FWF): W1230

For example, you may include a sentence such as "The author acknowledges the support of the Austrian Science Fund (FWF): W1230." Please do not forget!

Project 9:
Diophantine approximation and combinatorial problems

Publications 2018

[64] Niclas Technau, Diophantine approximation: Analytic and geometric methods, PhD thesis, TU Graz, (2018).
[bib]
[63] Christoph Aistleitner, Thomas Lachmann, Marc Munsch, Niclas Technau, Agamemnon Zafeiropoulos, The Duffin-Schaeffer conjecture with extra divergence, preprint, (2018).
[bib] [arXiv]
[62] Christoph Aistleitner, Thomas Lachmann, Marc Munsch, Niclas Technau, Agamemnon Zafeiropoulos, The Duffin-Schaeffer Conjecture with Extra Divergence, (2018). (preprint)
[bib] [arXiv]
[61] Carsten Elsner, Niclas Technau, On linear relations for Dirichlet series formed by recursive sequences of second order, preprint, (2018).
[bib] [arXiv]
[60] Kwok Chi Chim, István Pink, Volker Ziegler, On a variant of Pillai's problem II, J. Number Theory, 183, (2018).
[bib] [arXiv] [MR] [doi/article]
[59] Kwok Chi Chim, Linear forms in logarithms and applications to Diophantine problems, PhD thesis, TU Graz, (2018).
[bib]
[58] Christoph Aistleitner, Thomas Lachmann, Niclas Technau, There is no Khintchine threshold for metric pair correlations, (2018). (preprint)
[bib] [arXiv]
[57] Manfred Madritsch, Adrian-Maria Scheerer, Robert Tichy, Computable absolutely Pisot normal numbers, Acta Arithmetica, (2018). (to appear)
[bib] [arXiv] [doi/article]
[56] Dijana Kreso, Robert Tichy, Diophantine equations in separated variables, Period. Math. Hungar., 76(1), 47-67, (2018).
[bib] [arXiv] [doi/article]
[55] Mahadi Ddamulira, Florian Luca, On the $x$-coordinates of Pell equations which are $k$-generalized Fibonacci numbers, (2018). (preprint)
[bib] [arXiv]
[54] Mahadi Ddamulira, Carlos A. Gómez, Florian Luca, On a problem of Pillai with $k$--generalized Fibonacci numbers and powers of $2$, Monatshefte für Mathematik, (2018).
[bib] [arXiv] [doi/article]

Publications 2017

[53] Marc Technau, Niclas Technau, A Loewner Equation for Infinitely Many Slits, Computational Methods and Function Theory, 17, 255-272, (2017).
[bib] [MR] [doi/article]
[52] Adrian-Maria Scheerer, Dynamical systems and normal numbers -- qualitative and computational aspects, PhD thesis, TU Graz, (2017).
[bib]
[51] Adrian-Maria Scheerer, Computable Absolutely Normal Numbers and Discrepancies, Math. Comp., 86, 2911-2926, (2017).
[bib] [arXiv] [MR] [doi/article]
[50] Thomas Lachmann, Niclas Technau, On Exceptional Sets in the Metric Poissonian Pair Correlations problem, (2017). (preprint)
[bib] [arXiv]
[49] Christian Elsholtz, Marc Technau, Niclas Technau, The maximal order of iterated multiplicative functions, (2017). (preprint)
[bib] [arXiv]
[48] Kwok Chi Chim, Volker Ziegler, On Diophantine equations involving sums of Fibonacci numbers and powers of 2, (2017). (preprint)
[bib] [arXiv]
[47] Kwok Chi Chim, István Pink, Volker Ziegler, On a variant of Pillai's problem, Int. J. Number Theory, 13, 1711-1727, (2017).
[bib] [arXiv] [MR] [doi/article]
[46] Michael A. Bennett, Adrian-Maria Scheerer, Squares with three nonzero digits, Chapter in Number theory---Diophantine problems, uniform distribution and applications (C. Elsholtz, P. Grabner, eds.), Springer, Cham, 83—108, (2017).
[bib] [arXiv] [MR] [doi/article]
[45] Christoph Aistleitner, Verónica Becher, Adrian-Maria Scheerer, Theodore A. Slaman, On the construction of absolutely normal numbers, Acta Arith., 180(4), 333—346, (2017).
[bib] [arXiv] [MR] [doi/article]
[44] Michael Kerber, Robert Tichy, Mario Weitzer, Constrained Triangulations, Volumes of Polytopes, and Unit Equations, Chapter in 33rd International Symposium on Computational Geometry (SoCG 2017) (Boris Aronov, Matthew J. Katz, eds.), 77, 46:1—46:15, (2017).
[bib] [doi/article]
[43] Dijana Kreso, Diophantine equations in separated variables and lacunary polynomials, Int. J. Number Theory, 13(9), 2055-2074, (2017).
[bib] [MR] [doi/article]
[42] Christian Elsholtz, Niclas Technau, Robert Tichy, On the regularity of primes in arithmetic progressions, Int. J. Number Theory, 13(5), 1349-1361, (2017).
[bib] [arXiv] [MR] [doi/article]
[41] Mahadi Ddamulira, Florian Luca, Mihaja Rakotomalala, On a problem of Pillai with Fibonacci numbers and powers of $2$, Proc. Indian Acad. Sci. (Math. Sci.), 127(3), 411-421, (2017).
[bib] [arXiv] [MR] [doi/article]

Publications 2016

[40] Niclas Technau, Martin Widmer, On a Counting Theorem of Skriganov, (2016).
[bib] [arXiv]
[39] Art\=uras Dubickas, Dijana Kreso, Diophantine equations with truncated binomial polynomials, Indag. Math., 27(1), 392-405, (2016).
[bib] [MR] [doi/article]
[38] Manfred G. Madritsch, Robert F. Tichy, Multidimensional van der Corput sets and small fractional parts of polynomials, (2016). (preprint)
[bib] [arXiv]
[37] M. R. Iacò, W. Steiner, R. Tichy, Linear recursive odometers and beta-expansions, Unif. Distrib. Theory, 11(1), 175—186, (2016).
[bib] [MR] [doi/article]
[36] Mahadi Ddamulira, Florian Luca, Mihaja Rakotomalala, Fibonacci numbers which are products of two Pell numbers, The Fibonacci Quarterly, 54(1), 11-18, (2016).
[bib] [arXiv] [MR] [doi/article]
[35] I. Berkes, R. Tichy, The Kadec-Pełczyński theorem in $L^p$, $1\leq p<2$, Proc. Amer. Math. Soc., 144(5), 2053—2066, (2016).
[bib] [MR] [doi/article]
[34] Vladimir Balaz, Maria Rita Iacó, Oto Strauch, Stefan Thonhauser, Robert Tichy, An extremal problem in uniform distribution theory, Uniform distribution theory, 11(2), 1-21, (2016).
[bib]

Publications 2015

[33] Adrian-Maria Scheerer, Normality in Pisot numeration systems, Ergodic Theory and Dynamical Systems, 1-9, (2015).
[bib] [arXiv] [MR] [doi/article]
[32] Dijana Kreso, On common values of lacunary polynomials at integer points, New York J. Math., 21, 987—1001, (2015).
[bib] [MR] [doi/article]
[31] Maria Rita Iacò, Milan Pa\v stéka, Robert F. Tichy, Measure density for set decompositions and uniform distribution, Rend. Circ. Mat. Palermo (2), 64(2), 323—339, (2015).
[bib] [arXiv] [MR] [doi/article]
[30] Christian Elsholtz, Adam J. Harper, Additive decompositions of sets with restricted prime factors, Trans. Amer. Math. Soc., 367(10), 7403—7427, (2015).
[bib] [MR] [doi/article]
[29] Ante Ćustić, Lajos Hajdu, Dijana Kreso, Robert Tijdeman, On conjectures and problems of Ruzsa concerning difference graphs of S-units, Acta Math. Hungar., 146, 391-404, (2015).
[bib] [arXiv] [MR] [doi/article]
[28] Vladimír Balá\v z, Jana Fialová, Markus Hofer, Maria R. Iacò, Oto Strauch, The asymptotic distribution function of the 4-dimensional shifted van der Corput sequence, Tatra Mt. Math. Publ., 64, 75—92, (2015).
[bib] [MR] [doi/article]
[27] István Berkes, Robert Tichy, On permutation-invariance of limit theorems, J. Complexity, 31(3), 372—379, (2015).
[bib] [MR] [doi/article]
[26] István Berkes, Robert Tichy, Lacunary series and stable distributions, Chapter in Mathematical statistics and limit theorems, Springer, Cham, 7—19, (2015).
[bib] [MR] [doi/article]
[25] Fabrizio Barroero, Algebraic $S$-integers of fixed degree and bounded height, Acta Arithmetica, 167(1), 67—90, (2015).
[bib] [arXiv] [MR] [doi/article]
[24] Dijana Kreso, Robert F. Tichy, Functional composition of polynomials: indecomposability, Diophantine equations and lacunary polynomials, Grazer Math. Ber., 363, 143—170, (2015).
[bib] [arXiv] [MR]
[23] M. R. Iacò, S. Thonhauser, R. F. Tichy, Distribution functions, extremal limits and optimal transport, Indag. Math. (N.S.), 26(5), 823—841, (2015).
[bib] [arXiv] [MR] [doi/article]

Publications 2014

[22] Dijana Kreso, Michael E. Zieve, On factorizations of maps between curves, (2014). (preprint)
[bib] [arXiv]
[21] Dijana Kreso, Rational function decomposition and Diophantine equations, PhD thesis, TU Graz, (2014).
[bib] [doi/article]
[20] Maria Rita Iacó, Low discrepancy sequences: theory and applications, PhD thesis, Università della Calabria, (2014). ((cotutelle with TU Graz))
[bib] [arXiv]
[19] Markus Hofer, Maria Rita Iacò, Optimal bounds for integrals with respect to copulas and applications, Journal of Optimization Theory and Applications, 161, 999-1011, (2014).
[bib] [arXiv] [MR] [doi/article]
[18] Christian Elsholtz, Alan Filipin, Yasutsugu Fujita, On Diophantine quintuples and $D(-1)$-quadruples, Monatshefte für Mathematik, 175, 227-239, (2014).
[bib] [MR] [doi/article]
[17] Ingrid Carbone, Maria Rita Iacò, Aljo\v ca Volčič, A dynamical system approach to the Kakutani-Fibonacci sequence, Ergodic Theory Dynam. Systems, 34(6), 1794—1806, (2014).
[bib] [arXiv] [MR] [doi/article]
[16] Fabrizio Barroero, Martin Widmer, Counting lattice points and o-minimal structures, International Mathematics Research Notices, 2014, 4932-4957, (2014).
[bib] [arXiv] [MR] [doi/article]
[15] Fabrizio Barroero, Counting algebraic integers of fixed degree and bounded height, Monatshefte für Mathematik, 175, 25-41, (2014).
[bib] [arXiv] [MR] [doi/article]

Publications 2013

[14] Dijana Kreso, Csaba Rakaczki, Diophantine equations with Euler polynomials, Acta Arithmetica, 161, 267—281, (2013).
[bib] [arXiv] [MR] [doi/article]
[13] Markus Hofer, Maria Rita Iacò, Robert Tichy, Ergodic properties of $\beta$-adic Halton sequences, Ergodic Theory and Dynamical Systems, 35, 895—909, (2013).
[bib] [arXiv] [MR] [doi/article]
[12] Andrej Dujella, Christian Elsholtz, Sumsets being squares, Acta Mathematica Hungarica, 141(4), 353-357, (2013).
[bib] [MR] [doi/article]
[11] Rainer Dietmann, Christian Elsholtz, Igor E. Shparlinski, On gaps between primitive roots in the Hamming metric., Quarterly Journal of Mathematics, 64(4), 1043—1055, (2013).
[bib] [arXiv] [MR] [doi/article]
[10] Fabrizio Barroero, Counting lattice points, o-minimal structures and applications, PhD thesis, TU Graz, (2013).
[bib] [doi/article]

Publications 2012

[9] András Bazsó, Dijana Kreso, Florian Luca, Ákos Pintér, On equal values of power sums of arithmetic progressions, Glasnik Matematički, 47(2), 253—263, (2012).
[bib] [arXiv] [MR]
[8] Christoph Aistleitner, István Berkes, Robert Tichy, On the system $f(nx)$ and probabilistic number theory. Analytic and probabilistic methods in number theory, In Proceedings of the 5th International Conference in honour of J. Kubilius held in Palanga, TEV, 1-18, (2012).
[bib] [arXiv] [MR]
[7] Christoph Aistleitner, István Berkes, Robert Tichy, On the law of the iterated logarithm for permuted lacunary sequences, Proceedings of the Steklov Institute of Mathematics, 276, 3-20, (2012).
[bib] [arXiv] [MR]

Publications 2011

[6] Zrinka Franu\v sić, Dijana Kreso, Nonextensibility of the pair $\lbrace 1, 3\rbrace$ to a Diophantine quintuple in ${\mathbb Z}[\sqrt{2}]$, Journal of Combinatorics and Number Theory, 3(3), 1-15, (2011).
[bib] [arXiv] [MR]
[5] Christopher Frei, Sum of units in number fields and function fields, PhD thesis, TU Graz, (2011).
[bib] [doi/article]
[4] Fabrizio Barroero, Christopher Frei, Robert F. Tichy, Additive unit representations in rings over global fields -- A survey, Publicationes Mathematicae Debrecen, 79(3-4), 291-307, (2011).
[bib] [arXiv] [MR]
[3] Christoph Aistleitner, István Berkes, Robert Tichy, On the asymptotic behavior of weakly lacunary sequences, Proceedings of the American Mathematical Society, 139, 2505-2517, (2011).
[bib] [arXiv] [MR] [doi/article]

Publications 2010

[2] Dependence in Probability, Analysis and Number Theory, (István Berkes, Richard C. Bradley, Herold Dehling, Magda Peligrad, Robert Tichy, eds.), Kendrick Press, Heber City, UT, iv+353, (2010).
[bib]

Publications 201?

[1] Adrian-Maria Scheerer, On the continued fraction expansion of absolutely normal numbers, J. Th. Nombres Bordeaux, (201?). (to appear)
[bib] [arXiv]