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

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Levinson J., Miller S.

Acta Arithmetica

2013

tom 161

nr 2

145-182

Previous work by Rubinstein and Gao computed the n-level densities for families of quadratic Dirichlet L-functions for test functions f̂₁, ..., f̂ₙ supported in $∑_{i=1}^n |u_i| < 2$, and showed agreement with random matrix theory predictions in this range for n ≤ 3 but only in a restricted range for larger n. We extend these results and show agreement for n ≤ 7, 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.

Ograniczanie wyników

1 Acta Arithmetica

1 Levinson J.

1 Miller S.

1 2013

Wyniki wyszukiwania

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