Open Access
Oct. 2003 Zetas and moments of finite group actions
Kazufumi Kimoto
Proc. Japan Acad. Ser. A Math. Sci. 79(8): 128-133 (Oct. 2003). DOI: 10.3792/pjaa.79.128


We introduce and study two kinds of zeta functions $\zeta(u; G,X)$ and $Z(u; G,X)$ as well as moments $m(k; G,X)$ attached to a given finite group action $G \curvearrowright X$. We show that zeta functions determine the moments, and moments determine the multiple transitivity of the action. In the symmetric group case we give an explicit formula of moments and calculate zeta functions of the infinite symmetric group $\mathfrak{S}_{\infty}$.


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Kazufumi Kimoto. "Zetas and moments of finite group actions." Proc. Japan Acad. Ser. A Math. Sci. 79 (8) 128 - 133, Oct. 2003.


Published: Oct. 2003
First available in Project Euclid: 18 May 2005

zbMATH: 1063.11028
MathSciNet: MR2013092
Digital Object Identifier: 10.3792/pjaa.79.128

Primary: 16W22
Secondary: 11M99

Keywords: finite group actions , zeta functions

Rights: Copyright © 2003 The Japan Academy

Vol.79 • No. 8 • Oct. 2003
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