Low-lying zeros of L-functions for Quaternion Algebras
Number Theory
2020-11-02 v2
Abstract
The density conjecture of Katz and Sarnak predicts that, for natural families of L-functions, the distribution of zeros lying near the real axis is governed by a group of symmetry. In the case of the universal family of automorphic forms of bounded analytic conductor on a totally definite quaternion algebra, we determine the associated distribution for a restricted class of test functions. In particular it leads to non-trivial results on densities of non-vanishing at the central point.
Keywords
Cite
@article{arxiv.1810.13257,
title = {Low-lying zeros of L-functions for Quaternion Algebras},
author = {Didier Lesesvre},
journal= {arXiv preprint arXiv:1810.13257},
year = {2020}
}
Comments
to appear in Ann. Institut Fourier, 43 pages. arXiv admin note: text overlap with arXiv:1810.02787