The Weyl bound for triple product L-functions in the cubic level
Number Theory
2025-08-20 v1
Abstract
In this paper, we focus on the strong subconvexity bounds for triple product L-functions in the cubic level aspect. Our proof on the Weyl-type bound synthesizes techniques from classical analytic number theory with methods in automorphic forms and representation theory. The methods include the refined Petersson trace formula for the newforms of cubic level, classical Voronoi summation formula, Jutila's circle method, Kuznetsov trace formula and the spectral large sieve inequality.
Keywords
Cite
@article{arxiv.2508.13746,
title = {The Weyl bound for triple product L-functions in the cubic level},
author = {Xinchen Miao and Huimin Zhang},
journal= {arXiv preprint arXiv:2508.13746},
year = {2025}
}
Comments
32 pages. Comments are very welcome!