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

Alessandro Zaccagnini

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

Number Theory 2016-03-10 v1

Authors: Alessandro Zaccagnini

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.

Keywords

selberg integral pair-correlation function riemann zeta-function zeros of zeta prime number distribution short intervals

Cite

@article{arxiv.1603.02952,
  title  = {The Selberg integral and a new pair-correlation function for the zeros of the Riemann zeta-function},
  author = {Alessandro Zaccagnini},
  journal= {arXiv preprint arXiv:1603.02952},
  year   = {2016}
}

Comments

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

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