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Number Theory Seminar

Spectral reciprocity and nonvanishing of central L-values for GL(4) x GL(2)

Stephen D. Miller

Location:  Hill 425
Date & time: Tuesday, 14 November 2017 at 2:00PM - 3:00PM

Abstract: The combination of the Kuznetsov and Voronoi formulas has played a powerful role in analytic estimates of automorphic L-functions for GL(2), for example in the subconvexity problem.  The talk will discuss applications of a new combination of formulas for GL(4), which yields an identity equating sums of GL(4) x GL(2) L-values with other sums of the same type.  As an application, we show that for each self-dual cusp form F on GL(4,Z)GL(4,R) there exists infinitely many Maass forms f such that L(1/2,F x f) is nonzero.  Time permitting, I will explain why techniques used in the proof suggest that the GL(n) x GL(n-2) Converse Theorem of Cogdell & Piatetski-Shapiro is sharp.

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