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arXiv · 1208.0930

The n-level densities of low-lying zeros of quadratic Dirichlet L-functions

Jake Levinson·Steven J. Miller
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Abstract

Previous work by Rubinstein and Gao computed the n-level densities for families of quadratic Dirichlet L-functions for test functions where the sum of the supports of the Fourier transforms is at most 2, and showed agreement with random matrix theory predictions in this range for n < 4 but only in a restricted range for larger n. We extend these results and show agreement for n < 8, and reduce higher n to a Fourier transform identity. The proof involves adopting a new combinatorial perspective to convert all terms to a canonical form, which facilitates the comparison of the two sides.

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Jake Levinson, Steven J. Miller. 2014-04-02. The n-level densities of low-lying zeros of quadratic Dirichlet L-functions. https://arxiv.org/abs/1208.0930

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