Thue equations and the method of Coleman-Chabauty
Number Theory
2007-05-23 v1
Abstract
In this paper, we prove that a Thue equation F(x,y) = h, where h is an integer and F is a polynomial of degree n with integer coefficients and without repeated roots, has at most 2n^3 - 2n - 3 solutions provided that the Mordell-Weil rank of the Jacboian of the corresponding curve is less than (n-1)(n-2)/2. The proof uses the method of Coleman-Chabauty, extended here to apply to arbitrary regular models of curves, along with an explicit construction of a portion of a regular model for the curve corresponding to the Thue equation.
Keywords
Cite
@article{arxiv.math/0005186,
title = {Thue equations and the method of Coleman-Chabauty},
author = {Dino Lorenzini and Thomas J. Tucker},
journal= {arXiv preprint arXiv:math/0005186},
year = {2007}
}
Comments
30 pages