Back to Search
Start Over
Non-vanishing of Maass form L-functions at the central point.
- Source :
- Proceedings of the American Mathematical Society; 2/1/2021, Vol. 149 Issue 2, p509-523, 15p
- Publication Year :
- 2021
-
Abstract
- In this paper, we consider the family {L<subscript>j</subscript>(s)}<subscript>j=1</subscript><superscript>∞</superscript> of L-functions associated to an orthonormal basis {u<subscript>j</subscript>}<subscript>j=1</subscript><superscript>∞</superscript> of even Hecke-Maass forms for the modular group SL(2,Z) with eigenvalues {λ<subscript>j</subscript> = κ<subscript>j</subscript><superscript>2</superscript> + 1/4}<subscript>j=1</subscript><superscript>∞</superscript>. We prove the following effective non-vanishing result: At least 50 % of the central values L<subscript>j</subscript>(1/2) with κ<subscript>j</subscript> ≤ T do not vanish as T → ∞. Furthermore, we establish effective non-vanishing results in short intervals. [ABSTRACT FROM AUTHOR]
- Subjects :
- ORTHONORMAL basis
MODULAR forms
EIGENVALUES
L-functions
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 149
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 148035865
- Full Text :
- https://doi.org/10.1090/proc/15208