Low-lying zeros of L-functions for Quaternion Algebras

Didier Lesesvre

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arXiv · 1810.13257

Low-lying zeros of L-functions for Quaternion Algebras

Didier Lesesvre

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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.

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Didier Lesesvre. 2018-10-30. Low-lying zeros of L-functions for Quaternion Algebras. https://arxiv.org/abs/1810.13257

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