Moments of symmetric square L-functions
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<(2−δ)|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|(6/7−δ). This is joint work with Olga Balkanova.