Abstract. We give a new heuristic for all of the main terms in the integral moments of various families of primitive L-functions. The results agree with previous conjectures for the leading orderâ€¦ (More)

In this paper we present some evidence that methods from random matrix theory can give insight into the frequency of vanishing for quadratic twists of modular L-functions. The central question is theâ€¦ (More)

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(N), O(2N) and USp(2N). Inâ€¦ (More)

We examine the number of vanishings of quadratic twists of the L-function associated to an elliptic curve. Applying a conjecture for the full asymptotics of the moments of critical L-values we obtainâ€¦ (More)

In this paper, we obtain several expansions for Î¶(s) involving a sequence of polynomials in s, denoted by Î±k(s). These polynomials can be regarded as a generalization of Stirling numbers of the firstâ€¦ (More)

Characteristic polynomials of unitary matrices are extremely useful models for the Riemann zeta-function Î¶(s). The distribution of their eigenvalues give insight into the distribution of zeros of theâ€¦ (More)

We derive formulas for the terms in the conjectured asymptotic expansions of the moments, at the central point, of quadratic Dirichlet L-functions, L(1/2, Ï‡d), and also of the L-functions associatedâ€¦ (More)

We describe an algorithm for obtaining explicit expressions for lower terms for the conjectured full asymptotics of the moments of the Riemann zeta function, and give two distinct methods forâ€¦ (More)

Abstract. We investigate the moments of the derivative, on the unit circle, of characteristic polynomials of random unitary matrices and use this to formulate a conjecture for the moments of theâ€¦ (More)

Let q be an odd prime power, and Hq,d denote the set of square-free monic polynomials D(x)âˆˆFq[x] of degree d. Katz and Sarnak showed that the moments, over Hq,d, of the zeta functions associated toâ€¦ (More)