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April 2003 A note on Poincaré sums for finite groups
Takashi Ono
Proc. Japan Acad. Ser. A Math. Sci. 79(4): 95-97 (April 2003). DOI: 10.3792/pjaa.79.95


A simple and beautiful idea of Poincaré on Poincaré series in automorphic functions can be applied to an arbitrary ring $R$ acted by a group $G$. When $G$ is finite, the key is to look at the 0-dimensional Tate cohomology of $(G, R)$ twisted by the 1-cohomology class of the group of units of $R$. As a simplest case, we examine when $R$ is the ring of integers of a quadratic field.


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Takashi Ono. "A note on Poincaré sums for finite groups." Proc. Japan Acad. Ser. A Math. Sci. 79 (4) 95 - 97, April 2003.


Published: April 2003
First available in Project Euclid: 18 May 2005

zbMATH: 1099.11029
MathSciNet: MR1976364
Digital Object Identifier: 10.3792/pjaa.79.95

Primary: 11F75

Keywords: cohomology group , cohomology set , Finite group , Poincaré sum , quadratic field

Rights: Copyright © 2003 The Japan Academy

Vol.79 • No. 4 • April 2003
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