A unitary test of the Ratios Conjecture - Mathematics > Number TheoryReport as inadecuate




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Abstract: The Ratios Conjecture of Conrey, Farmer and Zirnbauer predicts the answers tonumerous questions in number theory, ranging from n-level densities andcorrelations to mollifiers to moments and vanishing at the central point. Theconjecture gives a recipe to generate these answers, which are believed to becorrect up to square-root cancelation. These predictions have been verified,for suitably restricted test functions, for the 1-level density of orthogonaland symplectic families of L-functions. In this paper we verify theconjecture-s predictions for the unitary family of all Dirichlet $L$-functionswith prime conductor; we show square-root agreement between prediction andnumber theory if the support of the Fourier transform of the test function isin -1,1, and for support up to -2,2 we show agreement up to a power savingsin the family-s cardinality.



Author: John Goes, Steven Jackson, Steven J. Miller, David Montague, Kesinee Ninsuwan, Ryan Peckner, Thuy Pham

Source: https://arxiv.org/







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