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

Jake Levinson, and Steven J. Miller. "The n-level densities of low-lying zeros of quadratic Dirichlet L-functions." Acta Arithmetica 161.2 (2013): 145-182. <http://eudml.org/doc/279719>.

@article{JakeLevinson2013,
abstract = {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.},
author = {Jake Levinson, Steven J. Miller},
journal = {Acta Arithmetica},
keywords = {Dirichlet -function; zeros; quadratic character; -level density; random matrix theory},
language = {eng},
number = {2},
pages = {145-182},
title = {The n-level densities of low-lying zeros of quadratic Dirichlet L-functions},
url = {http://eudml.org/doc/279719},
volume = {161},
year = {2013},
}

TY - JOUR
AU - Jake Levinson
AU - Steven J. Miller
TI - The n-level densities of low-lying zeros of quadratic Dirichlet L-functions
JO - Acta Arithmetica
PY - 2013
VL - 161
IS - 2
SP - 145
EP - 182
AB - 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.
LA - eng
KW - Dirichlet -function; zeros; quadratic character; -level density; random matrix theory
UR - http://eudml.org/doc/279719
ER -