Non-vanishing of Maass form L-functions at the critical point

2018/10/18 by Olga Balkanova, Bingrong Huang, Balkanova, Olga +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1810.07991

openalex publication_date 2018/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the family \L_j(s)\_j=1^∞ of L-functions associated to an orthonormal basis \u_j\_j=1^∞ of even Hecke-Maass forms for the modular group SL(2, Z) with eigenvalues \λ_j=κ_j²+1/4\_j=1^∞. We prove the following effective non-vanishing result: At least 50 % of the central values L_j(1/2) with κ_j ≤ T do not vanish as T→ ∞. Furthermore, we establish effective non-vanishing results in short intervals.

Citations

• Heegner points, cycles and Maass forms

Cited by

• On the Effective Non-vanishing of Hecke--Maass L-functions at Special Points

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