Low-lying zeros of $L$-functions for Maass forms over imaginary quadratic fields
Number Theory
2020-03-31 v2
Abstract
We study the - or -level density of families of -functions for Hecke--Maass forms over an imaginary quadratic field . For test functions whose Fourier transform is supported in , we prove that the -level density for Hecke--Maass forms over of square-free level , as tends to infinity, agrees with that of the orthogonal random matrix ensembles. For Hecke--Maass forms over of full level, we prove similar statements for the - and -level densities, as the Laplace eigenvalues tends to infinity.
Keywords
Cite
@article{arxiv.1908.06348,
title = {Low-lying zeros of $L$-functions for Maass forms over imaginary quadratic fields},
author = {Sheng-Chi Liu and Zhi Qi},
journal= {arXiv preprint arXiv:1908.06348},
year = {2020}
}
Comments
27 pages. To appear in Mathematika. RH added in the assumptions of Theorem A.1