Publications

  1. Two-step nilpotent extensions are not anabelian (with C. Pagano)
    arXiv, submitted.
  2. A note on the Hasse norm principle (with N. Rome)
    arXiv, submitted.
  3. Weak approximation on the norm one torus (with N. Rome)
    arXiv, submitted.
  4. On Stevenhagen's conjecture (with C. Pagano)
    arXiv, submitted.
  5. On Malle's conjecture for nilpotent groups (with C. Pagano)
    arXiv, To Appear in Transactions of the American Mathematical Society.
  6. Malle's conjecture for nonic Heisenberg extensions (with E. Fouvry)
    arXiv, submitted.
  7. The 4-rank of class groups of K(sqrt(n)) (with A. Morgan and H. Smit)
    arXiv, submitted.
  8. A sharp upper bound for the 2-torsion of class groups of multiquadratic fields (with C. Pagano)
    Mathematika, 68(2022), 237-258. [arXiv:2009.08399]
  9. Higher Rédei reciprocity and integral points on conics (with C. Pagano)
    arXiv.
  10. Effective convergence of coranks of random Rédei matrices (with C. Pagano)
    arXiv.
  11. On the 4-rank of class groups of Dirichlet biquadratic fields (with E. Fouvry and C. Pagano)
    Journal of the Institute of Mathematics of Jussieu, 21(2022), 1543-1570. [arXiv:2003.11406]
  12. On Dirichlet biquadratic fields (with E. Fouvry)
    arXiv, To Appear in Journal de Théorie des Nombres de Bordeaux.
  13. Higher genus theory (with C. Pagano)
    International Mathematics Research Notices, 4(2022), 2772-2823. [arXiv:1909.13871]
  14. The 8-rank of the narrow class group and the negative Pell equation (with S. Chan, D. Milovic and C. Pagano)
    Forum of Mathematics, Sigma, 10(2022), E46, 1-46. [arXiv:1908.01752]
  15. On the distribution of Cl(K)[l^infty] for degree l cyclic fields (with C. Pagano)
    Journal of the European Mathematical Society, 24(2022), 1189–1283. [arXiv:1812.06884]
  16. Joint distribution of spins (with D. Milovic)
    Duke Mathematical Journal, 170(2021), 1723-1755. [arXiv:1809.09597]
  17. The 16-rank of Q(-p)
    Algebra and Number Theory, 14(2020), 37-65. [arXiv:1809.07167]
  18. Unit equations and Fermat surfaces in positive characteristic (with C. Pagano)
    Acta Arithmetica, 193(2020), 133-156. [arXiv:1806.01614]
  19. Vinogradov's three primes theorem with primes having given primitive roots (with C. Frei and E. Sofos)
    Mathematical Proceedings of the Cambridge Philosophical Society, 170(2021), 75-110. [arXiv:1804.00573]
  20. Spins of prime ideals and the negative Pell equation x^2 - 2py^2 = -1 (with D. Milovic)
    Compositio Mathematica, 155(2019), 100-125. [arXiv:1611.10337]
  21. On the 16-rank of class groups of Q(-2p) for primes p = 1 mod 4 (with D. Milovic)
    International Mathematics Research Notices, 23(2019), 7406-7427. [arXiv:1705.05505]
  22. On the equation x_1 + x_2 = 1 in finitely generated multiplicative groups in positive characteristic (with C. Pagano)
    The Quarterly Journal of Mathematics, 68(2017), 923-934. [arXiv:1610.08377]
  23. The generalized Catalan equation in positive characteristic
    International Journal of Number Theory, 18(2022), 269-276. [arXiv:1610.06448]
  24. The Catalan equation
    Indagationes Mathematicae, 28(2017), 321-352. [arXiv:1610.06440]

Coauthors

Stephanie Chan, Etienne Fouvry, Christopher Frei, Djordjo Milovic, Adam Morgan, Carlo Pagano, Nick Rome, Mark Shusterman, Harry Smit, Efthymios Sofos.

Theses

Diophantine equations in positive characteristic (PhD thesis)
The Catalan equation (master thesis)
Irreducible polynomials (bachelor thesis, Dutch)

Notes on exponential equations in function fields

The Fermat-Catalan equation
Brocard's problem
Power equation
Plain Academic