The second moment of the $GL_3$ standard $L$-function on the critical line
Number Theory
2024-07-10 v1
Abstract
We obtain a strong bound on the second moment of the standard -function on the critical line. The method builds on the recent work of Aggarwal, Leung, and Munshi which treated shorter intervals. We deduce some corollaries including an improvement on the error term in the Rankin-Selberg problem, and on certain subconvexity bounds for and -functions. As a byproduct of the method of proof, we also obtain an estimate for an average of shifted convolution sums of Fourier coefficients.
Cite
@article{arxiv.2407.06962,
title = {The second moment of the $GL_3$ standard $L$-function on the critical line},
author = {Agniva Dasgupta and Wing Hong Leung and Matthew P. Young},
journal= {arXiv preprint arXiv:2407.06962},
year = {2024}
}