English

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

R2 v1 2026-07-22T17:30:42.609Z