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

Alessandro Languasco, Alessandro Zaccagnini

Published 2012-12-22, updated 2012-12-29Version 2

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.