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
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by Amir Akbary and Kyle Hambrook PDF

Math. Comp. 84 (2015), 1901-1932 Request permission

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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