Title: Nonvanishing theorems for twisted L-functions on unitary groups,
Abstract: We prove the nonvanishing of the twisted central critical values of a class
of automorphic L-functions for twists by all but finitely many unitary
characters in particular infinite families. The methods build on a
non-archimedean approach introduced by Greenberg in the context of the Birch
and Swinnerton-Dyer Conjecture. While this paper focuses on L-functions
associated to certain automorphic representations of unitary groups, it
illustrates how decades-old methods from Iwasawa theory can be combined with
the output of new machinery to achieve broader nonvanishing results.