Perturbation of zeros of the Selberg zeta-function for Γ₀(4)

2012/01/11 by Roelof Bruggeman, Roelof W. Bruggeman, Markus Fraczek +5
Mathematics · #11F72 #11M36 #37C30 #Advanced Algebra and Geometry #Analytic Number Theory Research #Dynamical Systems (math.DS) #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #advanced mathematical theories #math.DS #math.NT #msc:11F72 #msc:11M36 #msc:37C30

paper · pdf · doi:10.48550/arxiv.1201.2324

arxiv created 2012/01/11 · openalex publication_date 2012/01/11 · arxiv updated 2012/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the asymptotic behavior of zeros of the Selberg zeta-function for the congruence subgroup Γ₀(4) as a function of a one-parameter family of characters tending to the trivial character. The motivation for the study comes from observations based on numerical computations. Some of the observed phenomena lead to precise theorems that we prove and compare with the original numerical results.

Related

• Higher Selberg zeta functions for congruence subgroups
• Zeros of the extended Selberg class zeta-functions and of their derivatives
• Remarks on a special value of the Selberg zeta function
• Congruence properties of induced representations and their applications
• Selberg's zeta functions for congruence subgroups of modular groups in SL(2,R) and SL(2,C)