TITLE:
Primes in Arithmetic Progressions to Moduli with a Large Power Factor
AUTHORS:
Ruting Guo
KEYWORDS:
Primes; Arithmetic Progressions; Riemann Hypothesis
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.3 No.7A,
October
30,
2013
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.