Shabnam Akhtari
Research Interests
Number Theory, Diophantine Analysis, Geometry of Numbers.
Research Statement
Curriculum Vitae
My research is funded by the National Science Foundation grant DMS-1601837.
Some of my papers are available on
the arXiv .
Preprints and Publications in Refereed Journals
(with Kevser Aktas, Kirsti Biggs, Alia Hamieh, Kathleen Petersen and Lola Thompson) Lower Bounds for Heights in Relative Galois Extensions, submitted for publication in 2017. arXiv preprint
(with Manjul Bhargava) A positive proportion of locally soluble Thue equations are globally insoluble (preprint, 23 pages), submitted for publication in 2016. arXiv preprint
(with N. Saradha and D. Sharma) Thue's inequalities and the hypergeometric method , to appear in the Ramanujan Journal (2017) 45 pages. 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
Dissertations
Ph.D Thesis: Thue Equations and Related Topics, University of British Columbia, 2008.
M.Sc Thesis: Characterizing Cyclotomic Littlewood Polynomials, Simon Fraser University, 2004.
Links
Recent and Upcoming Trips