Explicit relations between primes in short intervals and exponential sums over primes
Copyright policy )Explicit relations between primes in short intervals and exponential sums over primes
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.
one reference corrected
- University of Padua Italy
- University of Parma Italy
Mathematics - Number Theory, pair-correlation conjecture, exponential sum over primes, 510, 11M26, exponential sums over primes , additive problems with primes, Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses, 11N05, Distribution of primes, primes in short intervals, 11M26, 11N05, 11M45, FOS: Mathematics, Number Theory (math.NT), 11M45, Sums over primes
Mathematics - Number Theory, pair-correlation conjecture, exponential sum over primes, 510, 11M26, exponential sums over primes , additive problems with primes, Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses, 11N05, Distribution of primes, primes in short intervals, 11M26, 11N05, 11M45, FOS: Mathematics, Number Theory (math.NT), 11M45, Sums over primes
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