28. Polynomial parametrization of SL₂ over global function field rings
Preprint (2026). arXiv:2610.12705
27. Local symbols and a first-order definition of the polynomial ring over an ultra-finite field in its fraction field
Accepted with revisions in ZML: Zeitschrift für Mathematische Logik und Grundlagen der Mathematik (2026). arXiv:2309.02738
26. Quaternionic analogues of Bers's theorem and Iss'sa's theorem
Submitted for publication (2025). arXiv:2107.11874
25. Ultra-Galois theory and an analogue of the Kronecker–Weber theorem for rational function fields over ultra-finite fields
Submitted for publication (2024). arXiv:2408.02158
24. Higher Reciprocity Laws and an analogue of the Grunwald–Wang theorem for the ring of polynomials over an ultrafinite field
Annals of Pure and Applied Logic, Volume 175, Issue 6 (2024), 103438. Publication · arXiv:2309.02734
23. On the generating polynomials for the distribution of generalized binomial coefficients in discrete valuation domains
Journal of Commutative Algebra, Volume 15 (2023), No. 1, 65–73.
22. (With Michael Larsen) Polynomial Parametrization for SL₂ over Quadratic Number Rings
International Mathematics Research Notices, Volume 2021, No. 9, 6993–7003. Publication
21. Effectively bounded idempotent generation of certain 2 × 2 matrices by idempotent matrices over real quadratic number rings
Submitted for publication. arXiv:2006.00733
20. Representation of units in cyclotomic function fields
International Journal of Number Theory, Vol.15, Number 7 (2019), 1385–1401.
19. (With Michael Larsen) Waring's problem for unipotent algebraic groups
Annales de L'Institut Fourier, Tome 69, n.4 (2019), 1857–1877.
18. The distribution of the Carlitz binomial coefficients modulo a prime
Annals of Combinatorics, Volume 22 (2018), Issue 3, pp 601–617.
17. A Carlitz module analogue of the Grunwald–Wang theorem
Indiana University Mathematics Journal, Volume 67 (2018), 1281–1297.
16. Certain forms violate the Hasse principle
Tokyo Journal of Mathematics, Volume 40 (2017), No. 1, 277–299.
15. Certain K3 surfaces parametrized by the Fibonacci sequence violate the Hasse principle
Rocky Mountain Journal of Mathematics, Volume 47 (2017), Number 5, 1693–1710.
14. The Brauer-Manin obstruction for certain quartic curves with negative discriminant
Communications in Algebra, 45 (2017), no. 2, 455–468.
13. Certain sets over function fields are polynomial families
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Volume XVII (2017), 205–230.
12. The classical umbral calculus, and the flow of a Drinfeld module
Transactions of the American Mathematical Society, Volume 369 (2017), no. 2, 1265–1289.
11. Some basic results in elementary number theory in function fields
Journal of Number Theory, 159 (2016), 295–306.
10. Function field analogues of Bang-Zsigmondy's theorem and Feit's theorem
Indiana University Mathematics Journal, Volume 65 (2016), Issue 6, 2081–2124.
9. Certain generalized Mordell curves over the rationals are pointless
Journal of the Australian Mathematical Society, 100 (2016), Issue 1, 42–64.
8. Non-vanishing of Carlitz-Fermat quotients modulo primes
Rocky Mountain Journal of Mathematics, Volume 46, Number 1 (2016), 125–130.
7. Algebraic families of hyperelliptic curves violating the Hasse principle
Pacific Journal of Mathematics, 274 (2015), no. 1, 141–182.
6. Carlitz module analogues of Mersenne primes, Wieferich primes, and certain prime elements in cyclotomic function fields
Journal of Number Theory, 145 (2014), 181–193.
5. From separable polynomials to nonexistence of rational points on certain hyperelliptic curves
Journal of the Australian Mathematical Society, 96 (2014), Issue 3, 354–385.
4. The Hasse principle for certain hyperelliptic curves and forms
The Quarterly Journal of Mathematics (Oxford), 64 (2013), no.1, 253–268. Publication
3. The arithmetic of certain quartic curves
Monatshefte für Mathematik, 168 (2012), no. 2, 191–214.
2. The arithmetic of certain del Pezzo surfaces and K3 surfaces
Journal de Théorie des Nombres de Bordeaux, 24 (2012), no.2, pp. 447–460. Publication
1. On the Hasse principle for certain quartic hypersurfaces
Proceedings of The American Mathematical Society, 139 (2011), no.12, pp. 4293–4305. Publication