Description
Online Number Theory Seminar
Abstract: Runge's method and Baker's methods for integral points can be combined to improve the general bound on the solutions of the $S$-unit equation $ax + by = 1$ (with the best explicit bound obtained by Győry in 2019). This leads to several applications including explicit $abc$ bounds and S-unit equations with unknowns in much larger groups. In this talk, I will explain how these are obtained and how the same ideas can be exploited for the $S$-unit equation $x^n + y = 1$. The current results are part of a joint work with Kálmán Győry.
For access please contact the organizers (ntrg[at]science.unideb.hu).