Moments of symmetric square L-functions

Speaker: Dmitry Frolenkov

Date: Tue, Feb 4, 2025

Location: Online, Zoom

Subject: Mathematics, Number Theory

Class: Scientific

CRG: L-Functions in Analytic Number Theory

Abstract:

I am going to discuss various results on moments of symmetric square L-functions and some of their applications. I will mainly focus on a recent result of R. Khan and M. Young and our improvement of it. Khan and Young proved a mean Lindelöf estimate for the second moment of Maass form symmetric-square L-functions L(sym2uj,1/2+it) on the short interval of length G>>|tj|(1+ϵ)/t(2/3), where tj is a spectral parameter of the corresponding Maass form. Their estimate yields a subconvexity estimate for L(sym2uj,1/2+it) as long as |tj|(6/7+δ)<<t<(2δ)|tj|. We obtain a mean Lindelöf estimate for the same moment in shorter intervals, namely for G>>|tj|(1+ϵ)/t. As a corollary, we prove a subconvexity estimate for L(sym2uj,1/2+it) on the interval |tj|(2/3+δ)<<t<<|tj|(6/7δ). This is joint work with Olga Balkanova.

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