The third moment of quadratic $L$-Functions
Speaker: Ian Whitehead
Date: Tue, Jul 26, 2022
Location: PIMS, University of Northern British Columbia
Conference: Moments of L-functions Workshop
Subject: Mathematics
Class: Scientific
CRG: L-Functions in Analytic Number Theory
Date: Tue, Jul 26, 2022
Location: PIMS, University of Northern British Columbia
Conference: Moments of L-functions Workshop
Subject: Mathematics
Class: Scientific
CRG: L-Functions in Analytic Number Theory
Abstract:
I will present a smoothed asymptotic formula for the third moment of Dirichlet $L$-functions associated to real characters. Beyond the main term, which was known, the formula has an unexpected secondary term of size $x^{3/4}$ and an error of size $x^{2/3}$. I will give background on the multiple Dirichlet series techniques that motivated this result. And I will describe the new ideas about local and global multiple Dirichlet series that made the final, sieving step in the proof possible. This is joint work with Adrian Diaconu.
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