Year: 2025
Type: article
Abstract: Let $F$ be a Hecke–Maaß cusp form for $SL(3,\mathbb{Z})$. We obtain the first non-trivial upper bound of the second moment of $L(F,s)$ in $t$-aspect: $$ \begin{align*} & \int_{T}^{2T}|L(F,1/2+it)|^2 dt\ll_{F,\varepsilon} T^{3/2-3/32+\varepsilon}.\end{align*} $$ Immediate corollaries include improvements over the existing results on the subconvexity bound for self-dual $GL(3)$ $L$-functions in the $t$-aspect and for self-dual $GL(3)\times GL(2)$ $L$-functions in the $GL(2)$ spectral aspect, the error term in the Rankin–Selberg problem, and the zero density estimate for $GL(3)$ $L$-functions.
Author: Sampurna Pal
Institution: Indian Statistical Institute
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Indian Statistical Institute
OpenAlex ID: W4413414171