Abstract
AbstractWe develop a derivative version of the relative trace formula on PGL(2) studied in our previous work, and derive an asymptotic formula of an average of central values (derivatives) of automorphicL-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.
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