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arXiv · 1212.5704

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

Alessandro Languasco·Alessandro Zaccagnini
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Abstract

Under the assumption of the Riemann Hypothesis (RH), 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.

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Alessandro Languasco, Alessandro Zaccagnini. 2012-12-29. Explicit relations between primes in short intervals and exponential sums over primes. https://doi.org/10.7169/facm%2F2014.51.2.9

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