Time

Feb 20 2006 - 5:30pm

Location

MW 154

Speaker

Taliesin Sutton (University of Wisconsin)

Abstract

Waldspurger generalized the Shimura correspondence to the adelic setting over any number field, he then used this correspondence to determine a necessary and sufficient condition for when the global theta lift of a half-integer weight automorphic representation is nonvanishing in terms of the central sign and symmetric central value of the L-function associated to the Shimura-Waldspurger lift. Using Howe's method of doubling, an extension of the Siegel-Weil formula, and the Rallis Basic Identity we will derive a new proof of this nonvanishing for the case when the central sign is 1. The proof also yields a formula for the symmetric central value of the above L-function, and can be explicitly computed when no local factors of the half-integer weight automorphic representation are supercuspidal.