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Texas A&M Number Theory Seminar

Department of Mathematics
Blocker 220
Wednesdays, 1:45–2:45 PM


Alex Dunn

UIUC

Wednesday, Janurary 22, 2020

Blocker 220, 1:45PM

Title: Moments of half integral weight modular L-functions, bilinear forms and applications

Abstract: Given a half-integral weight holomorphic newform f, we prove an asymptotic formula for the second moment of the twisted L-function over all primitive characters modulo a prime. In particular, we obtain a power saving error term and our result is unconditional; it does not rely on the Ramanujan-Petersson conjecture for the form f. This gives a very sharp Lindelöf on average result for L-series attached to Hecke eigenforms without an Euler product. The Lindelöf hypothesis for such series was originally conjectured by Hoffstein. In the course of the proof, one must treat a bilinear form in Salié sums. It turns out that such a bilinear form also has several arithmetic applications to equidistribution. These are a series of joint works with Zaharescu and Shparlinski-Zaharescu.