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 , 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa161-2-3,
author = {Jake Levinson and Steven J. Miller},
title = {The n-level densities of low-lying zeros of quadratic Dirichlet L-functions},
journal = {Acta Arithmetica},
volume = {161},
year = {2013},
pages = {145-182},
zbl = {1288.11085},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa161-2-3}
}
Jake Levinson; Steven J. Miller. The n-level densities of low-lying zeros of quadratic Dirichlet L-functions. Acta Arithmetica, Tome 161 (2013) pp. 145-182. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa161-2-3/