Authors and affiliations
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, … .
- Prime zeta function
- Riemman zeta function
- Prime numbers
- 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.
Cite this paperAPA
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.