Abstract: I will explain a new application of prehomogeneous zeta functions to non-vanishing of periods of automorphic forms. The zeta functions we use were first introduced by F. Sato and a general theory is developed by the recent work of Wen-Wei Li. They can be used to show non-vanishing of infinitely many toric periods of cuspidal representations of inner forms of GL(2). If time permits, I will mention future works based on the local theory of Wen-Wei Li. This is a joint work with Satoshi Wakatsuki.
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