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March 1999 A note on $q$-analogues of Dirichlet series
Hirofumi Tsumura
Proc. Japan Acad. Ser. A Math. Sci. 75(3): 23-25 (March 1999). DOI: 10.3792/pjaa.75.23


In this note, we study the $q$-Dirichlet series $Z_q(s)$ which was evaluated at non-positive integers by Satoh. We consider the values of $Z_q(s)$ at positive integers. By letting $q \to 1$, we get the Euler formulas for $\zeta(2k)$ and the recent formulas for $\zeta(2k+1)$ given by Cvijović-Klinowski. We also consider the relation between $Z_q(s)$ and Jackson's $q$-$\Gamma$-function.


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Hirofumi Tsumura. "A note on $q$-analogues of Dirichlet series." Proc. Japan Acad. Ser. A Math. Sci. 75 (3) 23 - 25, March 1999.


Published: March 1999
First available in Project Euclid: 23 May 2006

zbMATH: 0931.11031
MathSciNet: MR1700731
Digital Object Identifier: 10.3792/pjaa.75.23

Keywords: $q$-analogue , $q$-Benoulli numbers , Dirichlet series

Rights: Copyright © 1999 The Japan Academy

Vol.75 • No. 3 • March 1999
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