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