Illinois Journal of Mathematics

Thue equations and lattices

Jeffrey Lin Thunder

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Abstract

We consider Diophantine equations of the kind $|F(x,y)|=m$, where $F(X,Y)\in\mathbb{Z}[X,Y]$ is a homogeneous polynomial of degree at least 3 that has non-zero discriminant, $m$ is a fixed positive integer and $x,y$ are relatively prime integer solutions. Our results improve upon previous theorems due to Bombieri and Schmidt and also Stewart. We further provide reasonable heuristics for conjectures of Schmidt and Stewart regarding such equations.

Article information

Source
Illinois J. Math., Volume 59, Number 4 (2015), 999-1023.

Dates
Received: 15 March 2016
Revised: 4 November 2016
First available in Project Euclid: 27 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1488186018

Digital Object Identifier
doi:10.1215/ijm/1488186018

Mathematical Reviews number (MathSciNet)
MR3628298

Zentralblatt MATH identifier
06688853

Subjects
Primary: 11D75: Diophantine inequalities [See also 11J25] 11J25: Diophantine inequalities [See also 11D75]

Citation

Thunder, Jeffrey Lin. Thue equations and lattices. Illinois J. Math. 59 (2015), no. 4, 999--1023. doi:10.1215/ijm/1488186018. https://projecteuclid.org/euclid.ijm/1488186018


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