Functiones et Approximatio Commentarii Mathematici
- Funct. Approx. Comment. Math.
- Volume 51, Number 2 (2014), 379 -391.
Explicit relations between primes in short intervals and exponential sums over primes
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.
Funct. Approx. Comment. Math., Volume 51, Number 2 (2014), 379 -391.
First available in Project Euclid: 26 November 2014
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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. https://projecteuclid.org/euclid.facm/1417010860