On the Hecke Eigenvalues of Maass Forms

2014/05/20 by Wenzhi Luo, Luo, Wenzhi, Zhou, Fan
Mathematics · #11F12 (Secondary) #11F30 (Primary) 11F41 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1405.4937

openalex publication_date 2014/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let ϕ denote a primitive Hecke-Maass cusp form for Γ_o(N) with the Laplacian eigenvalue λ_ϕ=1/4+t_ϕ². In this work we show that there exists a prime p such that p\nmid N, |α_p|=|β_p| = 1, and p≪(N(1+|t_ϕ|))^c, where α_p, β_p are the Satake parameters of ϕ at p, and c is an absolute constant with 0

Citations

• La conjecture de Weil : I

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