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Explicit relations between pair correlation of zeros and primes in short intervals |
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| Authors: | Alessandro Languasco Alberto Perelli Alessandro Zaccagnini |
| Affiliation: | 1. Dipartimento di Matematica, Università di Padova, Via Trieste 63, 35121 Padova, Italy;2. Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, 16146 Genova, Italy;3. Dipartimento di Matematica, Università di Parma, Parco Area delle Scienze 53/a, Campus Universitario, 43124 Parma, Italy |
| Abstract: | In this paper we obtain a quantitative version of the well known theorem by Goldston and Montgomery about the equivalence between the asymptotic behaviors of the mean-square of primes in short intervals, and of the pair-correlation function of the zeros of the Riemann zeta function. |
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