We give a new heuristic for all of the main terms in the quotient of products of L-functions
averaged over a family. These conjectures generalize the recent conjectures for mean …

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 …

We review recent progress relating to the extreme value statistics of the characteristic
polynomials of random matrices associated with the classical compact groups, and of the …

We calculate the autocorrelation functions (or shifted moments) of the characteristic
polynomials of matrices drawn uniformly with respect to Haar measure from the groups U …

We use a smoothed version of the explicit formula to find an accurate pointwise
approximation to the Riemann zeta function as a product over its nontrivial zeros multiplied …

We reconsider the problem of calculating arbitrary negative integer moments of the
(regularised) characteristic polynomial for N× N random matrices taken from the Gaussian …

In random matrix theory, unitary ensembles of NN matrices H play a central role. 15 Such
ensembles are described by a measure d with finite moments R xkd (x), k 0, 1, 2,..., and the …

Random matrices and L-functions Page 1 Journal of Physics A: Mathematical and General
Random matrices and L-functions To cite this article: JP Keating and NC Snaith 2003 J. Phys …

Developments in random matrix theory Page 1 Journal of Physics A: Mathematical and General
INTRODUCTORY REVIEW Developments in random matrix theory To cite this article: PJ …

We prove that general correlation functions of both ratios and products of characteristic
polynomials of Hermitian random matrices are governed by integrable kernels of three …