A note on prime zeta function and Riemann zeta function

Mladen Vassilev–Missana
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 22, 2016, Number 4, Pages 12—15
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Authors and affiliations

Mladen Vassilev–Missana
5 Victor Hugo Str, Ap. 3
1124 Sofia, Bulgaria

Abstract

In the present paper, we first deduce a new recurrent formula, that connects P(s), P(2s) and ζ(s), where P(s) is the prime zeta function and ζ(s) is Riemann zeta function. After that, with the help of this recurrent formula, we find a new formula for P(s) expressing P(s) as infinite nested radicals (roots), depending on the values of ζ(2ks) for k = 0, 1, 2, 3, … .

Keywords

  • Prime zeta function
  • Riemman zeta function
  • Prime numbers

AMS Classification

  • 11A25
  • 11M06

References

  1. Glaisher, J. W. L. (1891) On the Sums of Inverse Powers of the Prime Numbers. Quart. J. Math., 25, 347–362.
  2. Froberg, C.-E. (1968) On the Prime Zeta Function. BIT 8, 187–202.
  3. Cohen, H. (2000) Advanced Topics in Computational Number Theory. New York: Springer-Verlag.

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Cite this paper

APA

Vassilev–Missana, M. (2016). A note on prime zeta function and Riemann zeta function. Notes on Number Theory and Discrete Mathematics, 22(4), 12-15.

Chicago

Vassilev–Missana, Mladen. “A Note on Prime Zeta Function and Riemann Zeta Function.” Notes on Number Theory and Discrete Mathematics 22, no. 4 (2016): 12-15.

MLA

Vassilev–Missana, Mladen. “A Note on Prime Zeta Function and Riemann Zeta Function.” Notes on Number Theory and Discrete Mathematics 22.4 (2016): 12-15. Print.

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