Type-I contributions to the one and two level densities of quadratic Dirichlet L–functions over function fields

Author: 

Bui, H
Florea, A
Keating, J

Publication Date: 

21 December 2020

Journal: 

Journal of Number Theory

Last Updated: 

2021-10-19T13:24:02.347+01:00

Volume: 

221

DOI: 

10.1016/j.jnt.2020.10.021

page: 

389-423

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 L–functions over function fields. We denote the various terms arising as Type-0, 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-0 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.

Symplectic id: 

1137903

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article