Moments of Central L-values for Maass Forms over Imaginary Quadratic Fields

2022/01/08 by Sheng‐Chi Liu, Liu, Sheng-Chi, Zhi Qi +1 · 1 citation
Mathematics · #11F12 #11F67 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2201.02900

openalex publication_date 2022/01/08 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

In this paper, over imaginary quadratic fields, we consider the family of L-functions L (s, f) for an orthonormal basis of spherical Hecke--Maass forms f with Archimedean parameter t_f. We establish asymptotic formulae for the twisted first and second moments of the central values L(\frac 1 2, f), which can be applied to prove that at least 33 % of L(\frac 1 2, f) with t_f \leqslant T are non-vanishing as T → ∞. Our main tools are the spherical Kuznetsov trace formula and the Vorono"i summation formula over imaginary quadratic fields.

Cited by

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

Related

• Proof of the Strong Ivić Conjecture for the Cubic Moment of Maass-form L-functions
• Low-lying zeros of L-functions for Maass forms over imaginary quadratic fields
• Non-vanishing of Maass form L-functions at the critical point
• The second moment of Maass form symmetric square L-functions at the central point
• Moments and Non-vanishing of central values of Quadratic Hecke L-functions in the Gaussian Field