n-Level Density of the Low-lying Zeros of Quadratic Dirichlet L-Functions
نویسندگان
چکیده
منابع مشابه
THE n-LEVEL DENSITIES OF LOW-LYING ZEROS OF QUADRATIC DIRICHLET L-FUNCTIONS
ABSTRACT. Previous work by Rubinstein [Rub] and Gao [Gao] computed the n-level densities for families of quadratic Dirichlet L-functions for test functions φ̂1, . . . , φ̂n supported in ∑ n i=1 |ui| < 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 hi...
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The statistics of low-lying zeros of quadratic Dirichlet L-functions were conjectured by Katz and Sarnak to be given by the scaling limit of eigenvalues from the unitary symplectic ensemble. The n-level densities were found to be in agreement with this in a certain neighborhood of the origin in the Fourier domain by Rubinstein in his Ph.D. thesis in 1998. An attempt to extend the neighborhood w...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2013
ISSN: 1687-0247,1073-7928
DOI: 10.1093/imrn/rns261