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

• Autorzy: Jake Levinson , Steven J. Miller
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11M50: Relations with random matrices
• 15B52: Random matrices
• 11M26: Nonreal zeros of ζ ( s ) and L ( s , χ ) ; Riemann and other hypotheses

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 161
• Numer: 2
• Strony: 145-182

Daty

wydano

2013

Twórcy

autor

Jake Levinson

• Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, U.S.A.

autor

Steven J. Miller

• Department of Mathematics and Statistics, Williams College, Williamstown, MA 01267, U.S.A.

Identyfikatory

DOI

10.4064/aa161-2-3