A note on Poincaré sums for finite groups
Ono, Takashi
Proc. Japan Acad. Ser. A Math. Sci., Tome 79 (2003) no. 3, p. 95-97 / Harvested from Project Euclid
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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.
Publié le : 2003-04-14
Classification:  Finite group,  cohomology set,  cohomology group,  Poincaré sum,  quadratic field,  11F75 
@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/