Skip to main content

On the prime zeta function

Abstract

The basic properties of the prime zeta function are discussed in some detail. A certain Dirichlet series closely connected with the function is introduced and investigated. Its dependence on the structure of the natural numbers with respect to their factorization is particularly stressed.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    Landau-Walfisz, Rend. di Palermo 44 (1919), p. 82–86.

    Google Scholar 

  2. 2.

    Davis,Table of the higher mathematical functions, II, p. 249, Bloomington 1935.

  3. 3.

    Glaisher, Quart. Jour. of Math. 25 (1891), p. 347.

    Google Scholar 

  4. 4.

    Haselgrove—Miller,Tables of the Riemann Zeta Function, Cambridge 1960.

  5. 5.

    Hardy—Wright,An Introduction to the Theory of Numbers, Oxford 1960.

  6. 6.

    Titchmarsh,The Theory of the Riemann Zeta Function, Oxford 1951.

Download references

Author information

Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Fröberg, CE. On the prime zeta function. BIT 8, 187–202 (1968). https://doi.org/10.1007/BF01933420

Download citation

Keywords

  • Computational Mathematic
  • Natural Number
  • Basic Property
  • Zeta Function
  • Dirichlet Series