Existence of Hilbert Cusp Forms with Non-vanishing<i>L</i>-values
Existence of Hilbert Cusp Forms with Non-vanishing<i>L</i>-values
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) …