## A variant of the Bombieri-Vinogradov theorem with explicit constants and applications.(English)Zbl 1341.11053

The authors give an effective version with explicit constants of a mean value theorem of R. C. Vaughan [J. Lond. Math. Soc., II. Ser. 6, 43–55 (1972; Zbl 0254.10040); ibid. II. Ser. 6, 326–328 (1973; Zbl 0254.10041)] related to the values of the twisted summatory function associated to the von Mangoldt function and a Dirichlet character. As a consequence, they prove an effective variant of the Bombieri-Vinogradov theorem with explicit constants. This effective variant can be used to obtain explicit results in many problems: as examples, the authors provide such results in several number theoretical problems related to shifted primes.

### MSC:

 11N13 Primes in congruence classes

### Citations:

Zbl 0254.10040; Zbl 0254.10041
Full Text:

### References:

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