Mathematical Research Letters

Volume 13 (2006)

Number 6

One-parameter families of unit equations

Pages: 935 – 945

DOI: http://dx.doi.org/10.4310/MRL.2006.v13.n6.a8

Author

Aaron Levin (Brown University)

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.

Full Text (PDF format)