Non-vanishing of maass form L-functions at the central point

Olga Balkanova, Bingrong Huang, Anders Södergren

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)509-523
Number of pages15
JournalProceedings of the American Mathematical Society
Issue number2
StatePublished - Feb 2021
Externally publishedYes


  • L-functions
  • Maass cusp forms
  • Mollification
  • Non-vanishing


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