Functiones et Approximatio Commentarii Mathematici

Explicit relations between primes in short intervals and exponential sums over primes

Alessandro Languasco and Alessandro Zaccagnini

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Under the assumption of the Riemann Hypothesis, we prove explicit quantitative relations between hypothetical error terms in the asymptotic formulae for truncated mean-square average of exponential sums over primes and in the mean-square of primes in short intervals. We also remark that such relations are connected with a more precise form of Montgomery's pair-correlation conjecture.

Article information

Funct. Approx. Comment. Math., Volume 51, Number 2 (2014), 379 -391.

First available in Project Euclid: 26 November 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11M26: Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses
Secondary: 11N05: Distribution of primes 11M45: Tauberian theorems [See also 40E05]

exponential sum over primes primes in short intervals pair-correlation conjecture


Languasco, Alessandro; Zaccagnini, Alessandro. Explicit relations between primes in short intervals and exponential sums over primes. Funct. Approx. Comment. Math. 51 (2014), no. 2, 379 --391. doi:10.7169/facm/2014.51.2.9.

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