THE n-LEVEL DENSITIES OF LOW-LYING ZEROS OF QUADRATIC DIRICHLET L-FUNCTIONS
نویسندگان
چکیده
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 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.
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