A note on the values of Zeta

Taekyun Kim and Seog-Hoon Rim
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 7, 2001, Number 2, Pages 32–35
Full paper (PDF, 432 Kb)


Authors and affiliations

Taekyun Kim
Institute of Science Education, Gongju National University
Chungnam Gongju, S. Korea

Seog-Hoon Rim
Department of Mathematics, Education Kyungpook University
Taegu 702-701. S. Korea


By q-calculation, we construct a q-analogue of Riemann ζ-function, Hurwitz’s zeta function and prove some formulas for the values of these functions. By using these formulae, we can evaluate the values of ζ(5) − Aζ(5, ¼) where A is some rational number.


  • Bernoulli number
  • Zeta function

AMS Classification

  • 11M41
  • 11B39


  1. T. Kim. On a q-analogue of the p-adic log gamma functions and related integrals J. Number Theory Vol. 76, 1999, 320-329.
  2. T. Kim. An invariant p-adic integral associated with Daehee numbers (to appear) in Integral. Trans. Special Function, 2001-2002.
  3. T. Kim. An explicit formula on the generalized Bernoulli number with order n. Indian J. of Pure and Applied Mathematics, Vol. 31, 2000, 1455-1461.
  4. J. Satho, q-Analogue of Riemann’s zeta-function and q-Euler numbers, J. Number Theory, Vol. 31, 1989, 346-362.


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Cite this paper

Kim, T., & Rim, S.-H. (2001). A note on the values of Zeta. Notes on Number Theory and Discrete Mathematics, 7(2), 32-35.

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