The Ramanujan-Petersson and Selberg conjectures for Maass forms

2020/01/29 by André Unterberger, Unterberger, Andr'e
Mathematics · #11F37 35S99 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2001.10956

openalex publication_date 2020/01/29 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We prove the Ramanujan-Petersson conjecture for Maass forms of the group SL(2,Z), with the help of automorphic distribution theory and pseudodifferential analysis. The first notion is an alternative to classical automorphic function theory, in which the plane takes the place usually ascribed to the hyperbolic half-plane. The Selberg conjecture for Hecke's group Γ₀(M) follows as well.

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