Multiplicative Dedekind η-function and representations of finite groups
Journal de Théorie des Nombres de Bordeaux, Volume 17 (2005) no. 1, pp. 359-380.

In this article we study the problem of finding such finite groups that the modular forms associated with all elements of these groups by means of a certain faithful representation belong to a special class of modular forms (so-called multiplicative η-products). This problem is open.

We find metacyclic groups with such property and describe the Sylow p-subgroups, p2, for such groups. We also give a review of the results about the connection between multiplicative η-products and elements of finite orders in SL(5,).

Dans cet article, nous étudions le problème de trouver des groupes finis tels que les formes modulaires associées aux éléments de ces groupes au moyen de certaines représentations fidèles appartiennent à des classes particulières de formes modulaires (appelées produits η multiplicatifs). Ce problème est ouvert.

Nous trouvons des groupes métacycliques ayant cette propriété et décrivons les p-sous-groupes de Sylow, p2, de tels groupes. Nous donnons également un aperçu des résulats reliant les produits η multiplicatifs et les éléments d’ordre fini de SL(5,).

Published online:
DOI: 10.5802/jtnb.495
Galina Valentinovna Voskresenskaya 1

1 Work position: Samara State University, the chair of algebra and geometry. Work address: 443011, Russia, Samara, acad.Pavlova street, house 1, room 406. Tel. (846-2) 34-54-38
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Galina Valentinovna Voskresenskaya. Multiplicative Dedekind $\eta $-function and representations of finite groups. Journal de Théorie des Nombres de Bordeaux, Volume 17 (2005) no. 1, pp. 359-380. doi : 10.5802/jtnb.495. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.495/

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