Explicit lower bounds on the modular degree of an elliptic curve

Details Explicit lower bounds on the modular degree of an elliptic curve Explicit lower bounds on the modular degree of an elliptic curve

2004-08-10

arxiv.org/abs/math/0408126v1

Mathematics

Number Theory

Scientific paper

We derive an explicit zero-free region for symmetric square L-functions of elliptic curves, and use this to derive an explicit lower bound for the modular degree of rational elliptic curves. The techniques are similar to those used in the classical derivation of zero-free regions for Dirichlet L-functions, but here, due to the work of Goldfield-Hoffstein-Lieman, we know that there are no Siegel zeros, which leads to a strengthened result.

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