Type-I contributions to the one and two level densities of quadratic Dirichlet $L$--functions over function fields
Number Theory
2020-01-13 v1
Abstract
Using the Ratios Conjecture, we write down precise formulas with lower order terms for the one and the two level densities of zeros of quadratic Dirichlet --functions over function fields. We denote the various terms arising as Type-, Type-I and Type-II contributions. When the support of the Fourier transform of the test function is sufficiently restricted, we rigorously compute the Type- and Type-I terms and confirm that they match the conjectured answer. When the restrictions on the support are relaxed, our results suggest that Type-II contributions become important in the two level density.
Keywords
Cite
@article{arxiv.2001.03265,
title = {Type-I contributions to the one and two level densities of quadratic Dirichlet $L$--functions over function fields},
author = {Hung M. Bui and Alexandra Florea and Jonathan Keating},
journal= {arXiv preprint arXiv:2001.03265},
year = {2020}
}
Comments
23 pages