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An extended pair-correlation conjecture and primes in short intervals


Authors: A. Languasco, A. Perelli and A. Zaccagnini
Journal: Trans. Amer. Math. Soc. 369 (2017), 4235-4250
MSC (2010): Primary 11M26, 11N05
DOI: https://doi.org/10.1090/tran/6835
Published electronically: December 27, 2016
MathSciNet review: 3624407
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Abstract: In this paper we extend the well-known investigations of Montgomery (1973) and Goldston and Montgomery (1987), concerning the pair-correlation function and its relations with the distribution of primes in short intervals, to a more general version of the pair-correlation function.


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A. Languasco
Affiliation: Dipartimento di Matematica Tullio Levi-Civita, Università di Padova, Via Trieste 63, 35121 Padova, Italy
Email: languasco@math.unipd.it

A. Perelli
Affiliation: Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, 16146 Genova, Italy
Email: perelli@dima.unige.it

A. Zaccagnini
Affiliation: Dipartimento di Matematica e Informatica, Università di Parma, Parco Area delle Scienze 53/a, 43124 Parma, Italy
Email: alessandro.zaccagnini@unipr.it

DOI: https://doi.org/10.1090/tran/6835
Keywords: Riemann zeta-function, pair correlation of zeros, primes in short intervals
Received by editor(s): March 30, 2014
Received by editor(s) in revised form: January 24, 2015, and June 18, 2015
Published electronically: December 27, 2016
Article copyright: © Copyright 2016 American Mathematical Society