Exploring the q-Riemann Zeta function and q-Bernoulli polynomials

T. Kim, C. S. Ryoo, L. C. Jang and S. H. Rim
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 11, 2005, Number 1, Pages 7–19
Full paper (PDF, 334 Kb)

Details

Authors and affiliations

T. Kim
Institute of Science Education
Kongju National University, Kongju 314-701, Korea

C. S. Ryoo
Department of Mathematics,
Hannam University, Daejeon 306-791, Korea

L. C. Jang
Department of Mathematics and Compute Science,
KonKuk University, Choongju 380-701, Korea

S. H. Rim
Department of Mathematics Education,
Kyungpook University, Daegu 702-701, Korea

Abstract

In this paper we study that the q-Bernoulli polynomial, which were constructed by T.Kim, are analytic continued to β_s(z). A new formula for the q-Riemann Zeta function ζ_,(s) due to T.Kim (see [1,2,8]) in terms of nested series of ζ_,(n) is derived. The new concept of dynamics of the zeros of analytic continued polynomials is introduced, and an investing phenomenon of ‘scattering’ of the zeros of β_s(z) is observed. Following the idea of q-zeta function due to T.Kim, we are going to use “Mathematica” to explore a formula for ζ_,(n).

Keywords

• q-Bernoulli polynomial
• q-Riemann Zeta function

AMS Classification

• 11B68
• 11S40

References

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