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.
Explicit relations between primes in short intervals and exponential sums over primes / A., Languasco; ZACCAGNINI, Alessandro. - In: FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI. - ISSN 0208-6573. - 51:2(2014), pp. 379-391. [10.7169/facm/2014.51.2.9]
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