Low-lying zeros of quadratic Dirichlet L-functions: A transition in the ratios conjecture
Journal article, 2018

We study the 1-level density of low-lying zeros of quadratic Dirichlet L-functions by applying the L-functions Ratios Conjecture. We observe a transition in the main term as was predicted by the Katz-Sarnak heuristic as well as in the lower-order terms when the support of the Fourier transform of the corresponding test function reaches the point 1. Our results are consistent with those obtained in previous work under GRH and are furthermore analogous to results of Rudnick in the function field case.


Daniel Fiorilli

University of Ottawa, Canada

James Parks

Royal Institute of Technology (KTH)

Anders Södergren

Chalmers, Mathematical Sciences, Algebra and geometry

University of Gothenburg

Quarterly Journal of Mathematics

0033-5606 (ISSN) 1464-3847 (eISSN)

Vol. 69 4 1129-1149

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