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arXiv:1406.2902 [math.NT]AbstractReferencesReviewsResources

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

Shingo Sugiyama, Masao Tsuzuki

Published 2014-06-11Version 1

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.

Categories: math.NT
Subjects: 11F67, 11F72
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