Preprints and Publications in Refereed Journal

Quartic index form equations and monogenizations of quartic orders, accepted for publication in Essential Number Theory (2022), arXiv preprint.   (link to a talk about this work in Number Theory Web Seminar).

Appendix to On the number of monogenizations of a quartic order, by Manjul Bhargava, arXiv preprint.

(with Jeffrey Vaaler) Heights, Regulators and Schinzel’s determinant inequality, II, submitted for publication, arXiv preprint

(with Jeffrey Vaaler) Lower bounds for regulators of number fields in terms of their discriminants, submitted for publication, accepted for publication in Journal de Theorie des Nombres de Bordeaux (2022) arXiv preprint

(with Jeffrey Vaaler) Independent relative units of low height, accepted for publication in Acta Arithmetica (2021), arXiv preprint

A positive proportion of locally soluble quartic Thue equations are globally insoluble,  Mathematical Proceedings of the Cambridge Philosophical Society (2021)1-16 , arXiv preprint

(with Paloma Bengoechea) Representation of integers by sparse binary forms,  Transactions of the American Mathematical Society 74 (2021), 1687-1709 . arXiv preprint

Counting monogenic cubic orders, Combinatorial and Additive Number Theory III  (2020), 13-24.

(with Jeffrey Vaaler) Lower bounds for Mahler measure that depend on the number of monomials,  International Journal of Number Theory Vol. 15, No. 07, pp. 1425-1436 (2019) . arXiv preprint

(with Manjul Bhargava) A positive proportion of Thue equations fail the integral Hasse principle,  American Journal of Mathematics, Vol. 141, No. 2 (2019), 283-307, arXiv preprint

(with N. Saradha and D. Sharma) Thue’s inequalities and the hypergeometric method, the Ramanujan Journal (2018) 45: 521-567 . arXiv preprint

(with Jeffrey Vaaler) Minkowski’s theorem on independent conjugate units the European Journal of Mathematics, 3(1), 111-149 (2017). arXiv preprint

(with Jeffrey Vaaler) Heights, Regulators and Schinzel’s determinant inequality. Acta Arithmetica 172 (2016), 285-298. arXiv preprint

Representation of small integers by binary forms. The Quarterly Journal of Mathematics: Oxford Journals. (2015) 66 (4): 1009-1054. arXiv preprint

Integral points on a certain family of elliptic curves. Journal de Theorie des Nombres de Bordeaux. 27 no. 2 (2015), p. 353-373. arXiv preprint 

Cubic Thue inequalities with positive discriminant. Publicationes Mathematicae Debrecen. 83/4 (2013), 727-739. arXiv preprint

(with Chantal David, Heekyoung Hahn and Lola Thompson) Distribution of squarefree values of sequences associated with elliptic curves. Contemporary Mathematics, Amer. Math. Soc. Volume 606 (2013), 171-188. arXiv preprint 

Representation of unity by binary forms. Transactions of the American Mathematical Society. 364 (2012), 2129-2155. arXiv preprint

Upper bounds for the number of solutions to quartic Thue equations. International Journal of Number Theory. Volume 8, Issue 2 (2012), 335-360. arXiv preprint

(With N. Saradha) Irreducibility of some orthogonal polynomials. Indagationes Mathematicae. 21 (2011), 127-137. pdf

The method of Thue-Siegel for quartic forms. Acta Arithmetica. 141 (2010), no. 1, 1-31. arXiv preprint

(With Ryotaro Okazaki) Quartic Thue equations. Journal of Number Theory. 130 (2010) no. 1, 40-60.

The Diophantine equation aX^4 – bY^2 = 1. Journal fuer die reine und angewandte Mathematik (Crelle’s Journal). 630 (2009), 33-57. arXiv preprint  

Cubic Thue Equations. Publicationes Mathematicae Debrecen. 75 (2009), no. 3-4, 459-483. arXiv preprint

(with Alain Togbe and Gary Walsh) On the equation aX^4 – bY^2 = 2. Acta Arithmetica 131 (2008), 145-169. Addendum: Acta Arithmetica 137 (2009), 199-202.

(with Stephen Choi) On the cyclotomic Littlewood polynomials. Journal of Number Theory 128 (2008), no. 4, 884-894. pdf