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A note on p-adic Carlitz's q-Bernoulli numbers

Published online by Cambridge University Press:  17 April 2009

Taekyun Kim  and
Seog-Hoon Rim
Taekyun Kim
Affiliation:
Centre for Experimental and Constructive Mathematcs, Simon Fraser University, Burnaby, Canada, e-mail: [email protected]
Seog-Hoon Rim
Affiliation:
Department of Mathematics Education, Kyungpook National University, 702–701Taegu, South Korea
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Abstract

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In a recent paper I have shown that Carlitz's q-Bernoulli number can be represented as an integral by the q-analogue μq of the ordinary p-adic invariant measure. In the p-adic case, J. Satoh could not determine the generating function of q-Bernoulli numbers. In this paper, we give the generating function of q-Bernoulli numbers in the p-adic case.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 2 , October 2000 , pp. 227 - 234
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Kim, T., ‘On a q-analogue of the p-adic log gamma functions and related integrals’, J. Number Theory 76 (1999), 320–329.CrossRefGoogle Scholar
[2]Satoh, J., ‘q-Analogue of Riemann's ζ-function and q-Euler numbers’, J. Number Theory 31 (1989), 346–362.CrossRefGoogle Scholar