Weak subconvexity without a Ramanujan hypothesis
Number Theory
2019-05-29 v2
Abstract
We describe a new method to obtain weak subconvexity bounds for -functions with mild hypotheses on the size of the Dirichlet coefficients. We verify these hypotheses for all automorphic -functions and (with mild restrictions) the Rankin-Selberg -functions attached to two automorphic representations. The proof relies on a new unconditional log-free zero density estimate for Rankin-Selberg -functions.
Cite
@article{arxiv.1804.03654,
title = {Weak subconvexity without a Ramanujan hypothesis},
author = {Kannan Soundararajan and Jesse Thorner},
journal= {arXiv preprint arXiv:1804.03654},
year = {2019}
}
Comments
25 pages. Appendix by Farrell Brumley. Referee comments incorporated