Hybrid subconvexity for Maass form symmetric-square L-functions

2024/08/13 by Balkanova, Olga, Frolenkov, Dmitry
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2408.06735

Abstract

Recently R. Khan and M. Young proved a mean Lindelöf estimate for the second moment of Maass form symmetric-square L-functions L(sym² u_j,1/2+it) on the short interval of length G≫ |t_j|^1+ε/t^2/3, where t_j is a spectral parameter of the corresponding Maass form. Their estimate yields a subconvexity estimate for L(sym² u_j,1/2+it) as long as |t_j|^6/7+δ ≪ t<(2-δ)|t_j|. We obtain a mean Lindelöf estimate for the same moment in shorter intervals, namely for G≫ |t_j|^1+ε/t. As a corollary, we prove a subconvexity estimate for L(sym² u_j,1/2+it) on the interval |t_j|^2/3+δ≪ t≪ |t_j|^6/7-δ.

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