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

Akbary, Amir; Hambrook, Kyle

doi:10.1090/S0025-5718-2014-02919-0

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

Authors: Amir Akbary and Kyle Hambrook
Journal: Math. Comp. 84 (2015), 1901-1932
MSC (2010): Primary 11N13
DOI: https://doi.org/10.1090/S0025-5718-2014-02919-0
Published electronically: December 29, 2014
MathSciNet review: 3335897
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Abstract | References | Similar Articles | Additional Information

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.

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