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arXiv · 1406.2902

Existence of Hilbert cusp forms with non-vanishing $L$-values

Shingo Sugiyama·Masao Tsuzuki
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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 $L$-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.

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Shingo Sugiyama, Masao Tsuzuki. 2014-06-11. Existence of Hilbert cusp forms with non-vanishing $L$-values. https://doi.org/10.4153/cjm-2015-048-4

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