The Weyl bound for triple product L-functions in the cubic level

TL;DR

This paper establishes a Weyl-type subconvexity bound for triple product L-functions in the cubic level aspect, combining advanced techniques from analytic number theory and automorphic forms.

Contribution

It introduces a novel approach to bounding triple product L-functions in the cubic level case using a combination of trace formulas and summation formulas.

Findings

Proved a Weyl-type bound for triple product L-functions in cubic level

Developed refined trace formula techniques for cubic level automorphic forms

Integrated multiple advanced methods to achieve strong subconvexity bounds

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.