Asymptotic densities of newforms

2002/01/04 by Morten S. Risager, Morten Skarsholm Risager, Risager, Morten Skarsholm
Mathematics · #11F12 (Primary) 11F72 #11F25 (Secondary) #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Spectral Theory (math.SP) #math.NT #math.SP #msc:11F12 #msc:11F25 #msc:11F72

paper · pdf · doi:10.48550/arxiv.math/0201029

arxiv created 2002/01/04 · openalex publication_date 2002/01/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define the counting function for non-analytic (Maass) newforms of Hecke congruence groups_Gamma₀(M)_. We then calculate the three main terms of this counting function and give necessary and sufficient conditions on M for this counting function to have the same shape as if it were counting eigenvalues related to a cocompact group.

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