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A note on the congruent distribution of the number of prime factors of natural numbers

Published online by Cambridge University Press:  22 January 2016

Tomio Kubota  and
Mariko Yoshida
Tomio Kubota
Affiliation:
Department of Mathematics, Meijo University, Shiogamaguchi 1-501, Tempaku-ku, Nagoya, 468-8502, Japan
Mariko Yoshida
Affiliation:
Department of Mathematics, Meijo University, Shiogamaguchi 1-501, Tempaku-ku, Nagoya, 468-8502, Japan
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Abstract

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Let n = p1p2 … pr be a product of r prime numbers which are not necessarily different. We define then an arithmetic function µm(n) by

where m is a natural number. We further define the function L(s, µm) by the Dirichlet series

and will show that L(s, µm), (m ≥ 3), has an infinitely many valued analytic continuation into the half plane Re s > ½.

Keywords

11N3711M41
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 163 , September 2001 , pp. 1 - 11
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2001

References

[1] Edwards, H. M., Riemann’s zeta function, Academic Press, 1974.Google Scholar
[2] Lang, S., Algebraic number theory, Addison Wesley, 1970.Google Scholar