Investigations of zeros near the central point of elliptic curve -functions (with an appendix by Eduardo Dueñez).
An identity for sums of polylogarithm functions.
Lower order terms in the 1-level density for families of holomorphic cuspidal newforms
The n-level densities of low-lying zeros of quadratic Dirichlet L-functions
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,...
An orthogonal test of the L-functions Ratios Conjecture, II
Benford's law, values of L-functions and the 3x+1 problem
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