In this article, we show to which extent one can improve a theorem of Bombieri, Friedlander and Iwaniec by using Hooley's variant of the divisor switching technique. We also give an application of the theorem in question, which is a Bombieri-Vinogradov type theorem for the Tichmarsh divisor problem in arithmetic progressions.

Keywords:

primes in arithmetic progressions, Titchmarsh divisor problem primes in arithmetic progressions, Titchmarsh divisor problem

MSC Classifications:

11N13 show english descriptions Primes in progressions [See also 11B25] 11N13 - Primes in progressions [See also 11B25]

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