Moments of quadratic Dirichlet $L$-functions over function fields

Date(s): Tuesday 18th February 2025 (14:00-15:00)
Contact: Event Convenor Contact: Hamid.Abban@nottingham.ac.uk
Description: Speaker's Name: Alexandru Popa
Speaker's Affiliation: Romainian Academy
Speaker's Research Theme(s): Pure Mathematics,
Abstract:
After reviewing recent progress in the moment problem, I will present an asymptotic formula for a "smoothed" fourth moment of quadratic Dirichlet L-functions over function fields, exhibiting infinitely many terms in the asymptotic expansion. The proof involves studying the multiple Dirichlet series associated with the fourth moment, a series in five complex variables satisfying an infinite group of functional equations. We show that this series can be analytically continued to an optimal domain, using a new type of functional equation. This is joint work with Adrian Diaconu and Vicenţiu Paşol.

Venue: MATHS A17

School of Mathematical Sciences

The University of Nottingham
University Park
Nottingham, NG7 2RD

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