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October 11, 2025Open Access

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

Key Points

The study establishes new strong subconvexity bounds for triple product L-functions at the cubic level, enhancing previous results.
The proof incorporates advanced techniques including the Petersson trace formula and Kuznetsov trace formula for thorough analysis.
The findings suggest significant implications in both analytic number theory and representation theory, leading to broader applications.
Employing methods like the Voronoi summation formula, the research presents a comprehensive approach to these complex functions.

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.

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Cite This Study

Miao et al. (Tue,) studied this question.

synapsesocial.com/papers/68e9b2e4ba7d64b6fc13314d https://doi.org/https://doi.org/10.48550/arxiv.2508.13746

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