One-Level density for holomorphic cusp forms of arbitrary level
Number Theory
2017-07-14 v4 Mathematical Physics
math.MP
Abstract
In 2000 Iwaniec, Luo, and Sarnak proved for certain families of -functions associated to holomorphic newforms of square-free level that, under the Generalized Riemann Hypothesis, as the conductors tend to infinity the one-level density of their zeros matches the one-level density of eigenvalues of large random matrices from certain classical compact groups in the appropriate scaling limit. We remove the square-free restriction by obtaining a trace formula for arbitrary level by using a basis developed by Blomer and Mili\'cevi\'c, which is of use for other problems as well.
Cite
@article{arxiv.1604.03224,
title = {One-Level density for holomorphic cusp forms of arbitrary level},
author = {Owen Barrett and Paula Burkhardt and Jonathan DeWitt and Robert Dorward and Steven J. Miller},
journal= {arXiv preprint arXiv:1604.03224},
year = {2017}
}
Comments
Version 2.0, 26 pages