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Applications of the L-functions ratios conjectures

J. B. Conrey·N. C. Snaith
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Abstract

In upcoming papers by Conrey, Farmer and Zirnbauer there appear conjectural formulas for averages, over a family, of ratios of products of shifted L-functions. In this paper we will present various applications of these ratios conjectures to a wide variety of problems that are of interest in number theory, such as lower order terms in the zero statistics of L-functions, mollified moments of L-functions and discrete averages over zeros of the Riemann zeta function. In particular, using the ratios conjectures we easily derive the answers to a number of notoriously difficult computations.

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J. B. Conrey, N. C. Snaith. 2007-07-20. Applications of the L-functions ratios conjectures. https://arxiv.org/abs/math/0509480

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