Applications of the L-functions ratios conjectures

Research paper by J. B. Conrey, N. C. Snaith

Indexed on: 20 Jul '07Published on: 20 Jul '07Published in: Mathematics - Number Theory


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.