Applications of the L-functions ratios conjectures

Details Applications of the L-functions ratios conjectures Applications of the L-functions ratios conjectures

2005-09-21

arxiv.org/abs/math/0509480v2

Proc. Lon. Math. Soc., Volume 93, No 3, 2007, pages 594--646

Mathematics

Number Theory

Scientific paper

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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