Advances in Pure Mathematics

Volume 3, Issue 7 (October 2013)

ISSN Print: 2160-0368   ISSN Online: 2160-0384

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Primes in Arithmetic Progressions to Moduli with a Large Power Factor

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DOI: 10.4236/apm.2013.37A003    3,947 Downloads   6,519 Views  Citations


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.

Share and Cite:

R. Guo, "Primes in Arithmetic Progressions to Moduli with a Large Power Factor," Advances in Pure Mathematics, Vol. 3 No. 7A, 2013, pp. 25-32. doi: 10.4236/apm.2013.37A003.

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