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A recurrence formula for \(q\)-Bernoulli numbers attached to formal group. (English) Zbl 1001.11011

The author introduces \(q\)-Bernoulli numbers attached to a formal group. For an appropriate case of the formal group law, this includes Carlitz’s \(q\)-Bernoulli numbers [L. Carlitz, Duke Math. J. 15, 987-1000 (1948; Zbl 0032.00304)]. In this framework an analog is proved of the recurrences for the Bernoulli numbers found by M. Kaneko [Proc. Japan Acad., Ser. A 71, 192-193 (1995; Zbl 0854.11012)].

MSC:

11B68 Bernoulli and Euler numbers and polynomials
05A30 \(q\)-calculus and related topics
14L05 Formal groups, \(p\)-divisible groups
Full Text: DOI

References:

[1] DOI: 10.3792/pjaa.71.192 · Zbl 0854.11012 · doi:10.3792/pjaa.71.192
[2] DOI: 10.1215/S0012-7094-48-01588-9 · Zbl 0032.00304 · doi:10.1215/S0012-7094-48-01588-9
[3] DOI: 10.1016/0022-314X(89)90078-4 · Zbl 0675.12010 · doi:10.1016/0022-314X(89)90078-4
[4] Japan. J. Math 20 pp 73– (1994)
[5] Nagoya Math. J 127 pp 129– (1992) · Zbl 0761.11023 · doi:10.1017/S002776300000413X
[6] Preprint Ser. in Math. Sciences, Nagoya Univ (1999)
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