@article{5ec34d65a46b48fab21812aede1308c5,
title = "Type-I contributions to the one and two level densities of quadratic Dirichlet L-functions over function fields",
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.",
keywords = "Density, Function fields, L-function, Off-diagonal, Quadratic character, Zeros",
author = "Hung Bui and Alexandra Florea and Keating, {J. P.}",
note = "Funding Information: Acknowledgments. A. Florea gratefully acknowledges the support of an NSF Postdoctoral Fellowship during part of the research which led to this paper. J.P. Keating was supported by a Royal Society Wolfson Research Merit Award, EPSRC Programme Grant EP/K034383/1 LMF: L-Functions and Modular Forms, and by ERC Advanced Grant 740900 (LogCorRM). The authors would also like to thank Julio Andrade, Brian Conrey, Chantal David, Steve Gonek and Matilde Lal{\'i}n for many stimulating discussions and comments during SQuaRE meetings at AIM, as well as Zeev Rudnick for useful comments on the paper. Publisher Copyright: {\textcopyright} 2020 Elsevier Inc. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2021",
month = apr,
doi = "10.1016/j.jnt.2020.10.021",
language = "English",
volume = "221",
pages = "389--423",
journal = "Journal of Number Theory",
issn = "0022-314X",
publisher = "Elsevier BV",
}