English

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

Number Theory 2017-05-12 v2

Abstract

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.

Keywords

Cite

@article{arxiv.1212.5704,
  title  = {Explicit relations between primes in short intervals and exponential sums over primes},
  author = {Alessandro Languasco and Alessandro Zaccagnini},
  journal= {arXiv preprint arXiv:1212.5704},
  year   = {2017}
}

Comments

one reference corrected

R2 v1 2026-06-21T22:59:22.370Z