In this paper we obtain a quantitative version of the celebrated theorem by D.A. Goldston and H.L. 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.
Explicit relations between pair correlation of zeros and primes in short intervals
LANGUASCO, ALESSANDRO;
2012
Abstract
In this paper we obtain a quantitative version of the celebrated theorem by D.A. Goldston and H.L. 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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