On the critical line zeros of L -- functions attached to automorphic cusp forms

2012/12/12 by Irina Sergeevna Rezvyakova, Rezvyakova, Irina
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1212.2948

openalex publication_date 2012/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove for L-function attached to an automorphic cusp form for the Hecke congruence group Γ₀(D), which is also an eigenfunction of all the Hecke operators, that a positive proportion of its non-trivial zeros lie on the critical line. This result extends the work of J.L. Hafner of 1983 where the case of the full modular group is considered.

Related

• An explicit formula for Hecke L-functions
• Infinitely many zeros of additively twisted L-functions on the critical line
• Simultaneous nonvanishing of the Products of L-functions associated to elliptic cusp forms
• Uniform Bound for Hecke L-Functions
• Low-lying zeros of a large orthogonal family of automorphic L-functions