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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## Details

### 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*(2*s*) 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*(2* ^{k}s*) for

*k*= 0, 1, 2, 3, … .

### Keywords

- Prime zeta function
- Riemman zeta function
- Prime numbers

### AMS Classification

- 11A25
- 11M06

### References

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

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## Cite this paper

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

ChicagoVassilev–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.

MLAVassilev–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.