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.
@article{1116443661,
author = {Ono, Takashi},
title = {A note on Poincar\'e sums for finite groups},
journal = {Proc. Japan Acad. Ser. A Math. Sci.},
volume = {79},
number = {3},
year = {2003},
pages = { 95-97},
language = {en},
url = {http://dml.mathdoc.fr/item/1116443661}
}
Ono, Takashi. A note on Poincaré sums for finite groups. Proc. Japan Acad. Ser. A Math. Sci., Tome 79 (2003) no. 3, pp. 95-97. http://gdmltest.u-ga.fr/item/1116443661/