A vertical Sato-Tate law for GL(4)

2025/09/16 by Tian An Wong, Wong, Tian An
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2509.13256

openalex publication_date 2025/09/16 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

We establish a doubly-weighted vertical Sato-Tate law for GL(4) with explicit error terms. The main ingredient is an extension of the orthogonality relation for Maass cusp forms on GL(4) of Goldfeld, Stade, and Woodbury from spherical to general forms, and without their assumption of the Ramanujan conjecture for the error term.

Citations

• The relative trace formula in analytic number theory
• An orthogonality relation for GL(4,R)
• Applications of the Kuznetsov formula on GL(3): the level aspect

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