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

2020/01/10 by Bui, Hung M., Florea, Alexandra, Keating, Jonathan
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2001.03265

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.

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