Publications

1. Elliptic curves and spin (with P. V. Uttenthal)
   arXiv, submitted.
2. Sums of rational cubes and the 3-Selmer group (with A. Smith)
   arXiv, submitted.
3. Binary forms with the same value set III. The case of D3 and D6 (with E. Fouvry)
   arXiv, submitted.
4. Binary forms with the same value set II. The case of D4 (with E. Fouvry)
   arXiv, submitted.
5. Binary forms with the same value set I (with E. Fouvry)
   arXiv, submitted.
6. Binary quadratic forms with the same value set (with E. Fouvry)
   arXiv, submitted.
7. 6-torsion and integral points on quartic surfaces (with S. Chan, C. Pagano and E. Sofos)
   arXiv, submitted.
8. Averages of multiplicative functions along equidistributed sequences (with S. Chan, C. Pagano and E. Sofos)
   arXiv, submitted.
9. Bounds for moments of l-torsion in class groups (with J. Thorner)
   arXiv, To Appear in Mathematische Annalen.
10. Malle's conjecture for fair counting functions (with C. Pagano)
    arXiv, To Appear in Algebra and Number Theory.
11. Two-step nilpotent extensions are not anabelian (with C. Pagano)
    Mathematische Zeitschrift, 306(2024), article no. 31. [arXiv:2301.10342]
12. A note on the Hasse norm principle (with N. Rome)
    Bulletin of the London Mathematical Society, 56(2024), 1004-1013. [arXiv:2301.10136]
13. Weak approximation on the norm one torus (with N. Rome)
    Compositio Mathematica, 160(2024), 1304-1348. [arXiv:2211.05911]
14. On Stevenhagen's conjecture (with C. Pagano)
    arXiv, submitted.
15. On Malle's conjecture for nilpotent groups (with C. Pagano)
    Transactions of the American Mathematical Society Series B, 10(2023), 310-354. [arXiv:2103.17223]
16. Malle's conjecture for nonic Heisenberg extensions (with E. Fouvry)
    arXiv, submitted.
17. The 4-rank of class groups of K(sqrt(n)) (with A. Morgan and H. Smit)
    arXiv, submitted.
18. 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]
19. Higher Rédei reciprocity and integral points on conics (with C. Pagano)
    arXiv, superseded by [arXiv:2201.13424].
20. Effective convergence of coranks of random Rédei matrices (with C. Pagano)
    Acta Arithmetica, 212(2024), 337-358. [arXiv:2005.12899]
21. 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]
22. On Dirichlet biquadratic fields (with E. Fouvry)
    Journal de Théorie des Nombres de Bordeaux, 34(2022), 637-646. [arXiv:2001.05350]
23. Higher genus theory (with C. Pagano)
    International Mathematics Research Notices, 4(2022), 2772-2823. [arXiv:1909.13871]
24. 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]
25. 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]
26. Joint distribution of spins (with D. Milovic)
    Duke Mathematical Journal, 170(2021), 1723-1755. [arXiv:1809.09597]
27. The 16-rank of Q(-p)
    Algebra and Number Theory, 14(2020), 37-65. [arXiv:1809.07167]
28. Unit equations and Fermat surfaces in positive characteristic (with C. Pagano)
    Acta Arithmetica, 193(2020), 133-156. [arXiv:1806.01614]
29. 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]
30. 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]
31. 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]
32. 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]
33. The generalized Catalan equation in positive characteristic
    International Journal of Number Theory, 18(2022), 269-276. [arXiv:1610.06448]
34. The Catalan equation
    Indagationes Mathematicae, 28(2017), 321-352. [arXiv:1610.06440]

Past and future coauthors

Stephanie Chan, Etienne Fouvry, Christopher Frei, Yuan Liu, Djordjo Milovic, Adam Morgan, Carlo Pagano, Ross Paterson, Nick Rome, Tim Santens, Mark Shusterman, Alec Shute, Harry Smit, Alexander Smith, Efthymios Sofos, Jesse Thorner, Peter Vang Uttenthal.

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