Riv. Mat. Univ. Parma, Vol. 7, No. 1, 2016

Alessandro Zaccagnini[1]

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

Pages: 133-151
Accepted in revised form: 1 March 2016
Mathematics Subject Classification (2010): 11M26, 11N05.
Keywords: Riemann zeta-function, Selberg integral, Montgomery's pair-correlation function.
[1] : Dipartimento di Matematica e Informatica, Università di Parma, Parco Area delle Scienze 53/a, Parma, 43124 Italia

This research was partially supported by the grant PRIN2010-11, Arithmetic Algebraic Geometry and Number Theory.

Abstract: The present paper is a report on joint work with Alessandro Languasco and Alberto Perelli, collected in [10], [11] and [12], 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.

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