Computing L-series of hyperelliptic curves

TL;DR

This paper presents methods for computing the L-series coefficients of hyperelliptic curves over Q of genus up to 3, utilizing point counting, generic group algorithms, and p-adic techniques.

Contribution

It introduces a combined approach using point counting, group algorithms, and p-adic methods for efficient L-series computation of hyperelliptic curves.

Findings

Successful computation of L-series coefficients for genus up to 3

Demonstrated efficiency of combined computational methods

Provided new data for hyperelliptic curve L-series

Abstract

We discuss the computation of coefficients of the L-series associated to a hyperelliptic curve over Q of genus at most 3, using point counting, generic group algorithms, and p-adic methods.