**Number
Theory Home**
| **Number
Theory Seminar**
| **Department Home**

# 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.