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Existence of Hilbert Cusp Forms with Non-vanishing L-values

Published online by Cambridge University Press:  20 November 2018

Shingo Sugiyama
Institute of Mathematics for Industry, Kyushu University, 744 Motooka Nishi-ku Fukuoka 819-0395, Japan e-mail:
Masao Tsuzuki
Department of Science and Technology, Sophia University, Kioi-cho 7-1 Chiyoda-ku Tokyo 102-8554, Japan e-mail:
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We develop a derivative version of the relative trace formula on $\text{PGL}\left( 2 \right)$ studied in our previous work, and derive an asymptotic formula of an average of central values (derivatives) of automorphic $L$-functions for Hilbert cusp forms. As an application, we prove the existence of Hilbert cusp forms with non-vanishing central values (derivatives) such that the absolute degrees of their Hecke fields are arbitrarily large.

Research Article
Copyright © Canadian Mathematical Society 2016


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