An Isaac Newton Institute Workshop

Matrix Ensembles and L-Functions

Parametric RMT, discrete symmetries, and cross-correlations between zeros of L-functions.

12th July 2004

Author: I. Smolyarenko (Cambridge)

Abstract

I will describe numerical and analytical results on cross-correlations between zeros of different L-functions. By analogy with parametric spectral correlations in random matrix theory and in dynamical systems, these cross-correlations can be used to establish the concept of a "distance" in the space of (conjectural) generalised Riemann operators, and to gain some insight into their overall structure.