The Selberg integral and a new pair-correlation function for the zeros of the Riemann zeta-function

Abstract

The present paper is a report on joint work with Alessandro Languasco and Alberto Perelli on our recent investigations on the Selberg integral and its connections to Montgomery's pair-correlation function. We introduce a more general form of the Selberg integral and connect it to a new pair-correlation function, emphasising its relations to the distribution of prime numbers in short intervals.

Proceedings of the Third Italian Meeting in Number Theory, Pisa, September 2015. To appear in the "Rivista di Matematica dell'Universita` di Parma"