I am a number theorist at TU Graz. My research interests lie in arithmetic geometry and analytic as well as algebraic number theory.
Seminar
Journal articles
All of my papers are available on arXiv.org.
- Distribution of genus numbers of abelian number fields, with D. Loughran and R. Newton, J. London Math. Soc., to appear
(arXiv) - Constructing abelian extensions with prescribed norms, with R. Richard, Math. Comp. 91 (2022): 381-399
(arXiv, doi) - Arithmetic progressions in binary quadratic forms and norm forms, with C. Elsholtz, Bull. London Math. Soc. 51 (4): 595-602, 2019
(arXiv, doi) - Number fields with prescribed norms, with D. Loughran and R. Newton, with an appendix by Y. Harpaz and O. Wittenberg, Comment. Math. Helv. 97 (1), 133-181, 2022
(arXiv, doi) - Averages and higher moments for the ℓ-torsion in class groups, with M. Widmer, Math. Ann., 379(3), 1205-1229, 2021
(arXiv, doi) - Vinogradov's three primes theorem with primes having given primitive roots, with P. Koymans and E. Sofos, Math. Proc. Camb. Philos. Soc., 170(1): 75-110, 2021
(arXiv, doi) - Average bounds for the ℓ-torsion in class groups of cyclic extensions, with M. Widmer, Res. Number Theory (2018) 4:34
(arXiv, doi) - Rational points and non-anticanonical height functions, with D. Loughran, Proc. Amer. Math. Soc. 147 (2019): 3209-3223
(arXiv, doi) - Rational points of bounded height on general conic bundle surfaces, with D. Loughran and E. Sofos, Proc. London Math. Soc. 117 (2), 407-440, 2018
(arXiv, doi) - Generalised divisor sums of binary forms over number fields, with E. Sofos, J. Inst. Math. Jussieu 19 (1): 137-173, 2020
(arXiv, doi) - The Hasse norm principle for abelian extensions, with D. Loughran and R. Newton, Amer. J. Math 140 (6): 1639-1685, 2018
(arXiv, doi) - Forms of differing degrees over number fields, with M. Madritsch, Mathematika 63 (1): 92-123, 2017
(arXiv, doi) - Counting rational points on smooth cubic
surfaces, with E. Sofos, Math. Res. Lett. 23 (1): 127-143, 2016
(arXiv, doi) - O-minimality on twisted universal torsors and Manin's conjecture over number fields, with M. Pieropan, Ann. Sci. Éc. Norm. Supér. 49 (4):757-811, 2016
(arXiv, doi) - On Manin's conjecture for a certain singular cubic surface over imaginary quadratic fields, with U. Derenthal, Int. Math. Res. Not. IMRN 2015 (10): 2728-2750, 2015
(arXiv, doi) - On sums of S-integers of bounded norm, with R. F. Tichy and V. Ziegler, Monatsh. Math. 175 (2): 241-247, 2014
(arXiv, doi) - Counting imaginary quadratic points via universal torsors, II, with U. Derenthal, Math. Proc. Camb. Philos. Soc. 156 (3): 383-407, 2014
(arXiv, doi) - Counting imaginary quadratic points via universal torsors, with U. Derenthal, Compositio Math. 150 (10): 1631-1678, 2014
(arXiv, doi) - Schanuel's theorem for heights defined via extension fields, with M. Widmer, Ann. Sc. Norm. Super. Pisa Cl. Sci., Vol. XV (2016), 355-398, 2016
(arXiv, doi) - Counting rational points over number fields on a singular cubic surface, Algebra Number Theory 7 (6): 1451-1479, 2013
(arXiv, doi) - Additive unit representations in rings over global fields - A survey, with F. Barroero and R. F. Tichy, Publ. Math. Debrecen 79 (3-4): 291-307, 2011
(arXiv) - On rings of integers generated by their units, Bull. London Math. Soc. 44, 167-182, 2012
(arXiv, doi) - Sums of units in function fields II - The extension problem, Acta Arith. 149 (4): 361-369, 2011
(arXiv, doi) - Sums of units in function fields, Monatsh. Math. 164 (1): 39-54, 2011
(arXiv, doi) - Non-unique factorization of polynomials over residue class rings of the integers, with S. Frisch, Comm. Algebra, 39 (4): 1482-1490, 2011
(arXiv, doi)
Conference proceedings
- Some applications of o-minimality in quantitative arithmetic geometry, Mathematisches Forschungsinstitut Oberwolfach, Report No. 22/2017
- Divisor sums and rational points on conic bundle surfaces, Mathematisches Forschungsinstitut Oberwolfach, Report No. 53/2016