Hostname: page-component-7dd5485656-zklqj Total loading time: 0 Render date: 2025-10-31T04:13:32.319Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let n = p 1 p 2 … 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

Information

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