The cubic moment of L-functions for specified local component families

2025/06/17 by Hu, Yueke, Petrow, Ian, Young, Matthew P. · 2 citations
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2506.14741

Abstract

We prove Lindelöf-on-average upper bounds on the cubic moment of central values of L-functions over certain families of \rm PGL₂/ℚ automorphic representations π given by specifying the local representation π_p of π at finitely many primes. Such bounds were previously known in the case that π_p belongs to the principal series or is a ramified quadratic twist of the Steinberg representation; here we handle the supercuspidal case. Crucially, we use new Petersson/Bruggeman/Kuznetsov forumulas for supercuspidal local component families recently developed by the authors. As corollaries, we derive Weyl-strength subconvex bounds for central values of \rm PGL₂ L-functions in the square-full aspect, and in the depth aspect, or in a hybrid of these two situations. A special case of our results is the Weyl-subconvex bound for all cusp forms of level p². Previously, such a bound was only known for forms that are twists from level p, which cover roughly half of the level p² forms.

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• The Weyl bound for triple product L-functions in the cubic level
• On a Generalization of Motohashi's Formula: Non-archimedean Weight Functions

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