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]

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

ZACCAGNINI, Alessandro
2014

Abstract

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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2566044
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