Nonvanishing of twists of $L$-functions attached to Hilbert modular forms

TL;DR

This paper develops algorithms to compute central values of twisted $L$-functions for Hilbert modular forms, performs extensive computations, and compares results with heuristics and random matrix theory predictions.

Contribution

It introduces new algorithms for calculating twisted $L$-function central values and provides computational evidence supporting theoretical heuristics.

Findings

Algorithms successfully compute $L$-function central values.

Computational results align with random matrix theory predictions.

Provides data supporting conjectures on the distribution of $L$-values.

Abstract

We describe algorithms for computing central values of twists of $L$-functions associated to Hilbert modular forms, carry out such computations for a number of examples, and compare the results of these computations to some heuristics and predictions from random matrix theory.