Applications of the Lfunctions ratios conjectures
Abstract
In upcoming papers by Conrey, Farmer and Zirnbauer there appear conjectural formulas for averages, over a family, of ratios of products of shifted Lfunctions. 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 Lfunctions, mollified moments of Lfunctions 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 September 2005
 arXiv:
 arXiv:math/0509480
 Bibcode:
 2005math......9480C
 Keywords:

 Mathematics  Number Theory
 EPrint:
 Proc. Lon. Math. Soc., Volume 93, No 3, 2007, pages 594646