Hostname: page-component-77c89778f8-7drxs Total loading time: 0 Render date: 2024-07-18T09:30:01.748Z Has data issue: false hasContentIssue false
  • English
  • Français

On Values of the Riemann Zeta Function at Integral Arguments

Published online by Cambridge University Press:  20 November 2018

John A. Ewell
John A. Ewell*
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115., U. S. A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

For each nonnegative integer r,

is represented by a multiple series which is expressed in terms of rational numbers and the special values of the zeta function Thus, the set serves as a kind of basis for expressing all of the values

Keywords

Riemann Zeta Function10H0510H08.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 1 , 01 March 1991 , pp. 60 - 66
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Apery, R., Irrationalité de £ (2) etc, (3), Astérisque, Paris: Société Mathématique de France 61( 1979), 11–13.Google Scholar
2. Apostol, T.M., Introduction to Analytic Number Theory. Springer-Verlag, New York 1976.Google Scholar
3. Choe, Boo Rim, An Elementary Proof of, Amer. Math. Monthly, 94 (1987), 662–663.Google Scholar
4. Courant, R., Differential and Integral Calculus. Interscience, New York, 1957.Google Scholar
5. Ewell, J. A., A New Series Representation for £ (3), Amer. Math. Monthly, 97 (1990), 219–220.Google Scholar
6. Grosswald, E., Die Werte der Riemannschen Zeta Function an ungeraden Argumenstellen, Nachrichten der Akad. Wiss. Göttingen, Math. Phys. Kl. 11 (1970), 9–13.Google Scholar
7. Ramanujan, S., Notebooks of Srinivasa Ramanujan (2 volumes). Tata Institute of Fundamental Research, Bombay, 1957.Google Scholar
8. Terras, A., Some formulas for the Riemann Zeta Function at odd integer argument resulting from Fourier expansions of the Epstein Zeta Function, Acta Arith., XXIX(1976) 181–189.Google Scholar