A variant of the Bombieri-Vinogradov theorem with explicit constants and applications

2013/09/11 by Amir Akbary, Akbary, Amir, Kyle Hambrook +1 · 1 citation
Mathematics · #11N13 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11N13

paper · pdf · doi:10.48550/arxiv.1309.2730

arxiv created 2013/12/04 · arxiv updated 2013/12/05

Abstract

We give an effective version with explicit constants of a mean value theorem of Vaughan related to the values of ψ(y, χ), the twisted summatory function associated to the von Mangoldt function Λand a Dirichlet character χ. 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.

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• An effective Bombieri-Vinogradov error term for sifting problems

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