One-Parameter Families of Unit Equations
Number Theory
2007-05-23 v1
Abstract
We study one-parameter families of S-unit equations of the form f(t)u+g(t)v=h(t), where f, g, and h are univariate polynomials over a number field, t is an S-integer, and u and v are S-units. For many possible choices of f, g, and h, we are able to determine all but finitely many solutions to the corresponding one-parameter family of S-unit equations. The results are obtained as consequences of some recent results on integral points on surfaces.
Keywords
Cite
@article{arxiv.math/0601685,
title = {One-Parameter Families of Unit Equations},
author = {Aaron Levin},
journal= {arXiv preprint arXiv:math/0601685},
year = {2007}
}
Comments
10 pages