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

Sugiyama, Shingo ; Tsuzuki, Masao

Canadian journal of mathematics, Tome 68 (2016) no. 4, pp. 908-960

Résumé

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.

Détail

DOI : 10.4153/CJM-2015-048-4

Mots-clés : 11F67, 11F72, automorphic representations, relative trace formulas, central L–values, derivatives of L–functions

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