On A Generalization of Motohashi's Formula

2023/10/12 by Han Wu, Wu, Han · 1 citation
Mathematics · #Advanced Mathematical Identities #Advanced Mathematical Theories #FOS: Mathematics #Mathematical Inequalities and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2310.08236

openalex publication_date 2023/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a spectral reciprocity formula relating GL₃ × GL₂ with GL₃ × GL₁ and GL₁ moments of L-functions discovered by Kwan. Globally we give an adelic and distributional treatment. Our test automorphic function is of general type. To achieve this generality we develop an extension of the generalized Godement sections. Locally we give the weight function transforms in both directions for the fixed tempered representation Π of GL₃(F). We obtain the transform by a theory of the Voronoi--Hankel transforms, which extends Miller--Schmid's local theory of the Voronoi formula for GL_n.

Cited by

• On a Generalization of Motohashi's Formula: Non-archimedean Weight Functions

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