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
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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

Abstract

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.

Keywords

  • Bernoulli number
  • Zeta function

AMS Classification

  • 11M41
  • 11B39

References

  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

APA

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

Chicago

Kim, T, and Seog-Hoon Rim. “A Note on the Values of Zeta.” Notes on Number Theory and Discrete Mathematics 7, no. 2 (2001): 32-35.

MLA

Kim, T, and Seog-Hoon Rim. “A Note on the Values of Zeta.” Notes on Number Theory and Discrete Mathematics 7.2 (2001): 32-35. Print.

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