Discrete Dynamics in Nature and Society
Volume 2005 (2005), Issue 2, Pages 171-181
doi:10.1155/DDNS.2005.171

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

T. Kim,1 C. S. Ryoo,2 L. C. Jang,3 and S. H. Rim4

1Science Education Research Institute, Education Science Research Center, Kongju National University, Kongju 314-701, Korea
2Department of Mathematics, Hannam University, Daejeon 306-791, Korea
3Department of Mathematics and Computer Science, Konkuk University, Chungcheongbuk-do, Chungju-Si 380-701, Korea
4Department of Mathematics Education, Teachers' College Kyungpook National University, Daegu 702-701, Korea

Received 15 July 2004

Copyright © 2005 T. Kim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study that the q-Bernoulli polynomials, which were constructed by Kim, are analytic continued to βs(z). A new formula for the q-Riemann zeta function ζq(s) due to Kim in terms of nested series of ζq(n) is derived. The new concept of dynamics of the zeros of analytic continued polynomials is introduced, and an interesting phenomenon of “scattering” of the zeros of βs(z) is observed. Following the idea of q-zeta function due to Kim, we are going to use “Mathematica” to explore a formula for ζq(n).