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- W121182000 abstract "We study the distribution of the zeros near the central point for weighted and unweighted families of Dirichlet L-functions. As the conductors tend to infinity, the main term of the 1-level densities agrees with the scaling limit of unitary matrices for even C^2 test functions whose Fourier transforms are supported in (-2,2), supporting the Katz-Sarnak conjecture. The lower order terms agree with the prediction from the L-function Ratios Conjecture in the regime where both can be computed, though we are able to compute beyond square-root cancelation, thus going further than what the Ratios Conjecture can predict. We also investigate the consequences of conjectures about the modulus dependence in the error terms in the distribution of primes in residue classes. We show how some natural conjectures imply that the 1-level densities agree with unitary matrices for arbitrary support, while some weaker conjectures still give an improvement over (-2,2), allowing support up to (-4,4)." @default.
- W121182000 created "2016-06-24" @default.
- W121182000 creator A5009672436 @default.
- W121182000 creator A5049983178 @default.
- W121182000 date "2011-11-16" @default.
- W121182000 modified "2023-09-27" @default.
- W121182000 title "Low-lying zeros of Dirichlet L-functions" @default.
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