Non-vanishing of maass form L-functions at the central point
Journal article, 2021

In this paper, we consider the family {Lj(s)}∞j=1 of L-functions associated to an orthonormal basis {uj}∞j=1 of even Hecke-Maass forms for the modular group SL(2,Z) with eigenvalues {λj = κ2j + 1/4}∞j=1. We prove the following effective non-vanishing result: At least 50% of the central values Lj(1/2) with κj ≤ T do not vanish as T → ∞. Furthermore, we establish effective non-vanishing results in short intervals.

Maass cusp forms

L-functions

Non-vanishing

Mollification

Author

Olga Balkanova

Russian Academy of Sciences

Bingrong Huang

Shandong University

Anders Södergren

Chalmers, Mathematical Sciences, Algebra and geometry

University of Gothenburg

Published in

Proceedings of the American Mathematical Society

0002-9939 (ISSN) 1088-6826 (eISSN)

Vol. 149 Issue 2 p. 509-523

Categorizing

Subject Categories (SSIF 2011)

Algebra and Logic

Discrete Mathematics

Mathematical Analysis

Identifiers

DOI

10.1090/proc/15208

More information

Latest update

2/11/2021