Publications

  1. On Malle's conjecture for nilpotent groups, I (with C. Pagano)
    arXiv, submitted.
  2. Malle's conjecture for nonic Heisenberg extensions (with E. Fouvry)
    arXiv, submitted.
  3. The 4-rank of class groups of K(sqrt(n)) (with A. Morgan and H. Smit)
    arXiv, submitted.
  4. A sharp upper bound for the 2-torsion of class groups of multiquadratic fields (with C. Pagano)
    arXiv, submitted.
  5. Higher Rédei reciprocity and integral points on conics (with C. Pagano)
    arXiv.
  6. Effective convergence of coranks of random Rédei matrices (with C. Pagano)
    arXiv.
  7. 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, To Appear. [arXiv:2003.11406]
  8. On Dirichlet biquadratic fields (with E. Fouvry)
    arXiv, To Appear in Journal de Théorie des Nombres de Bordeaux.
  9. Higher genus theory (with C. Pagano)
    International Mathematics Research Notices, To Appear. [arXiv:1909.13871]
  10. On the negative Pell equation (with S. Chan, D. Milovic and C. Pagano)
    arXiv, submitted.
  11. On the distribution of Cl(K)[l^infty] for degree l cyclic fields (with C. Pagano)
    arXiv, To Appear in Journal of the European Mathematical Society.
  12. Joint distribution of spins (with D. Milovic)
    Duke Mathematical Journal, 170(2021), 1723-1755. [arXiv:1809.09597]
  13. The 16-rank of Q(-p)
    Algebra and Number Theory, 14(2020), 37-65. [arXiv:1809.07167]
  14. Unit equations and Fermat surfaces in positive characteristic (with C. Pagano)
    Acta Arithmetica, 193(2020), 133-156. [arXiv:1806.01614]
  15. 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]
  16. 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]
  17. 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]
  18. 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]
  19. The generalized Catalan equation in positive characteristic
    arXiv, To Appear in International Journal of Number Theory.
  20. 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, 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