Title: The theta-period of a cuspidal automorphic representation of GL(n)
Speaker: Eyal Kaplan (OSU)
Seminar URL: https://research.math.osu.edu/numbertheory/
Abstract: Let E be an Eisenstein series corresponding to an automorphic cuspidal representation of GL(n), induced to a representation of SO(2n+1) through the Siegel parabolic subgroup. The presence of a pole of E at 1/2, that is, the nonvanishing of the residue E_{1/2} of E at 1/2, is determined by the presence of a pole of the partial symmetric square L-function at 1. We define a co-period integral of E, involving the integrationof E_{1/2} against a pair of automorphic forms in the space of the small representation of Bump, Friedberg and Ginzburg. We compute the co-period and relate it to a ``theta period" integral of GL(n) - an integral of a cusp form against two theta functions corresponding to the exceptional representation of Kazhdan and Patterson.
