Primes in Arithmetic Progressions to Moduli with a Large Power Factor

Ruting Guo

Network Center, Shandong University, Jinan, China.

DOI: 10.4236/apm.2013.37A003                

Abstract

Recently Elliott studied the distribution of primes in arithmetic progressions whose moduli can be divisible by highpowers of a given integer and showed that for integer a≥2 and real number A＞0. There is a B=B(A)＞0 such that

,

holds uniformly for moduli that are powers of a. In this paper we are able to improve his result.

Keywords

Primes; Arithmetic Progressions; Riemann Hypothesis

Conflicts of Interest

The authors declare no conflicts of interest.

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