## Number Theory Seminar

**Date: ** January 22, 2020

**Time: ** 1:45PM - 2:45PM

**Location: ** BLOC 220

**Speaker: **Alex Dunn, UIUC

**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.

**URL: ***Link*