Hostname: page-component-848d4c4894-hfldf Total loading time: 0 Render date: 2024-05-17T15:53:45.334Z Has data issue: false hasContentIssue false
  • English
  • Français

A recurrence formula for q-Bernoulli numbers attached to formal group

Published online by Cambridge University Press:  22 January 2016

Junya Satoh
Junya Satoh*
Affiliation:
Graduate School of Human Informatics, Nagoya University, Furo-cho Chikusa-ku, Nagoya 464-8601, Japan, jsatoh@math.human.nagoya-u.ac.jp
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.

Kaneko [2] proved a new recurrence formula for the Bernoulli numbers and gave two proofs. One of them was due to Don Zagier. We shall apply Zagier’s idea to the g-Bernoulli numbers attached to formal group.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 157 , 2000 , pp. 93 - 101
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2000

References

[1] Carlitz, L., q-Bernoulli numbers and polynomials, J. Duke Math. J., 15 (1948), 987–1000.Google Scholar
[2] Kaneko, M., A recurrence formula for the Bernoulli numbers, Proc. Japan Acad., 71, Ser. A, No. 8 (1995), 192–193.Google Scholar
[3] Satoh, J., q-analogue of Riemann’s ζ-function and q-Euler numbers, J. Number Theory, 31 (1989), 346–362.CrossRefGoogle Scholar
[4] Satoh, J., A construction of q-analogue of Dedekind sums, Nagoya Math. J, 127 (1992), 129–143.CrossRefGoogle Scholar
[5] Satoh, J., Construction of q-analogue by using Stirling numbers, Japan. J. Math., 20, No. 1 (1994), 73–91.CrossRefGoogle Scholar
[6] Satoh, J., Another look at the q-analogue from the viewpoint of formal groups, Preprint Ser. in Math. Sciences, Nagoya Univ. (1999-4).Google Scholar