A general S-unit equation solver and tables of elliptic curves over number fields

Abstract: In this talk we present work in progress on a new highly optimized solver for general and constraint S-unit equations over number fields. It has diophantine applications including asymptotic Fermat theorems, Siegel's method for computing integral points, and most strikingly for computing large tables of elliptic curves over number fields with good reduction outside given sets of primes S. For the latter, we improved on the method of Koutsianas (Parshin, Shafarevich, Elkies).

number theory

Audience: researchers in the topic

( slides | video )

Rational Points and Galois Representations

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