Applications of the L-functions ratios conjectures
Number Theory
2011-11-09 v2
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.
Cite
@article{arxiv.math/0509480,
title = {Applications of the L-functions ratios conjectures},
author = {J. B. Conrey and N. C. Snaith},
journal= {arXiv preprint arXiv:math/0509480},
year = {2011}
}