A variant of the Bombieri-Vinogradov theorem with explicit constants and applications
Number Theory
2013-12-05 v2
Abstract
We give an effective version with explicit constants of a mean value theorem of Vaughan related to the values of \psi(y, \chi), the twisted summatory function associated to the von Mangoldt function \Lambda and a Dirichlet character \chi. As a consequence of this result we prove an effective variant of the Bombieri-Vinogradov theorem with explicit constants. This effective variant has the potential to provide explicit results in many problems. We give examples of such results in several number theoretical problems related to shifted primes.
Keywords
Cite
@article{arxiv.1309.2730,
title = {A variant of the Bombieri-Vinogradov theorem with explicit constants and applications},
author = {Amir Akbary and Kyle Hambrook},
journal= {arXiv preprint arXiv:1309.2730},
year = {2013}
}