I am a number theorist at TU Graz. My research interests lie in arithmetic geometry and analytic as well as algebraic number theory.



Seminar

Graz-ISTA Number Theory Days



Journal articles

All of my papers are available on arXiv.org.

  1. Constructing abelian extensions with prescribed norms, with R. Richard, Math. Comp. 91 (2022): 381-399
    (arXiv, doi)
  2. Arithmetic progressions in binary quadratic forms and norm forms, with C. Elsholtz, Bull. London Math. Soc. 51 (4): 595-602, 2019
    (arXiv, doi)
  3. 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)
  4. Averages and higher moments for the ℓ-torsion in class groups, with M. Widmer, Math. Ann., 379(3), 1205-1229, 2021
    (arXiv, doi)
  5. 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)
  6. Average bounds for the ℓ-torsion in class groups of cyclic extensions, with M. Widmer, Res. Number Theory (2018) 4:34
    (arXiv, doi)
  7. Rational points and non-anticanonical height functions, with D. Loughran, Proc. Amer. Math. Soc. 147 (2019): 3209-3223
    (arXiv, doi)
  8. 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)
  9. Generalised divisor sums of binary forms over number fields, with E. Sofos, J. Inst. Math. Jussieu 19 (1): 137-173, 2020
    (arXiv, doi)
  10. The Hasse norm principle for abelian extensions, with D. Loughran and R. Newton, Amer. J. Math 140 (6): 1639-1685, 2018
    (arXiv, doi)
  11. Forms of differing degrees over number fields, with M. Madritsch, Mathematika 63 (1): 92-123, 2017
    (arXiv, doi)
  12. Counting rational points on smooth cubic surfaces, with E. Sofos, Math. Res. Lett. 23 (1): 127-143, 2016
    (arXiv, doi)
  13. 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)
  14. 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)
  15. On sums of S-integers of bounded norm, with R. F. Tichy and V. Ziegler, Monatsh. Math. 175 (2): 241-247, 2014
    (arXiv, doi)
  16. Counting imaginary quadratic points via universal torsors, II, with U. Derenthal, Math. Proc. Camb. Philos. Soc. 156 (3): 383-407, 2014
    (arXiv, doi)
  17. Counting imaginary quadratic points via universal torsors, with U. Derenthal, Compositio Math. 150 (10): 1631-1678, 2014
    (arXiv, doi)
  18. 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)
  19. Counting rational points over number fields on a singular cubic surface, Algebra Number Theory 7 (6): 1451-1479, 2013
    (arXiv, doi)
  20. 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)
  21. On rings of integers generated by their units, Bull. London Math. Soc. 44, 167-182, 2012
    (arXiv, doi)
  22. Sums of units in function fields II - The extension problem, Acta Arith. 149 (4): 361-369, 2011
    (arXiv, doi)
  23. Sums of units in function fields, Monatsh. Math. 164 (1): 39-54, 2011
    (arXiv, doi)
  24. 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

  1. Some applications of o-minimality in quantitative arithmetic geometry, Mathematisches Forschungsinstitut Oberwolfach, Report No. 22/2017
  2. Divisor sums and rational points on conic bundle surfaces, Mathematisches Forschungsinstitut Oberwolfach, Report No. 53/2016