Open Access
May 2004 A $q$-Mahler measure
Nobushige Kurokawa
Proc. Japan Acad. Ser. A Math. Sci. 80(5): 70-73 (May 2004). DOI: 10.3792/pjaa.80.70


We construct a $q$-analogue of the Mahler measure using a $q$-analogue of the logarithm. We present some basic examples, where we obtain $q$-analogues of special values of zeta functions. We calculate also the classical limit and the crystal limit.


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Nobushige Kurokawa. "A $q$-Mahler measure." Proc. Japan Acad. Ser. A Math. Sci. 80 (5) 70 - 73, May 2004.


Published: May 2004
First available in Project Euclid: 18 May 2005

zbMATH: 1060.11068
MathSciNet: MR2062804
Digital Object Identifier: 10.3792/pjaa.80.70

Primary: 11M06

Keywords: $q$-analogue , crystal , Mahler measure , zeta function

Rights: Copyright © 2004 The Japan Academy

Vol.80 • No. 5 • May 2004
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