Large spaces between the zeros of the Riemann zeta-function and random matrix theory

摘要

On the hypothesis that the 2k-th mixed moments of Hardy's Z-function and its derivative are correctly predicted by random matrix theory, it is established that large gaps (depending on, and apparently increasing with k) exist between the zeta zeros. The case k = 3 has been worked out in an earlier paper (in this journal) and the cases k = 4, 5, 6 are considered here. When k = 6 the gaps obtained have > 4 times the average gap length. This depends on calculations involving Jacobi-Schur functions and formulae for these functions due to Jacobi, Trudi and Aitken in the classical theory of equations. (C) 2004 Elsevier Inc. All rights reserved.