Existence of Hilbert cusp forms with non-vanishing $L$-values
Number Theory
2022-10-21 v1
Abstract
We give a derivative version of the relative trace formula on PGL(2) studied in our previous work, and obtain a formula of an average of central values (derivatives) of automorphic -functions for Hilbert cusp forms. As an application, we prove existence of Hilbert cusp forms with non-vanishing central values (derivatives) such that the absolute degrees of their Hecke fields are sufficiently large.
Cite
@article{arxiv.1406.2902,
title = {Existence of Hilbert cusp forms with non-vanishing $L$-values},
author = {Shingo Sugiyama and Masao Tsuzuki},
journal= {arXiv preprint arXiv:1406.2902},
year = {2022}
}