On the second moment for primes in an arithmetic progression
Number Theory
2015-06-26 v1
Abstract
Assuming the Generalized Riemann Hypothesis, we obtain a lower bound within a constant factor of the conjectured asymptotic result for the second moment for primes in an individual arithmetic progression in short intervals. Previous results were averaged over all progression of a given modulus. The method uses a short divisor sum approximation for the von Mangoldt function, together with some new results for binary correlations of this divisor sum approximation in arithmetic progressions.
Cite
@article{arxiv.math/0004149,
title = {On the second moment for primes in an arithmetic progression},
author = {Daniel Goldston and C. Y. Yildirim},
journal= {arXiv preprint arXiv:math/0004149},
year = {2015}
}