Multiplicative Dedekind η -function and representations of finite groups

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

Journal de Théorie des Nombres de Bordeaux (2005)

  • Volume: 17, Issue: 1, page 359-380
  • ISSN: 1246-7405

Abstract

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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, p ≠ 2 , for such groups. We also give a review of the results about the connection between multiplicative η -products and elements of finite orders in S L ( 5 , ℂ ) .

How to cite

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Voskresenskaya, Galina Valentinovna. "Multiplicative Dedekind $\eta $-function and representations of finite groups." Journal de Théorie des Nombres de Bordeaux 17.1 (2005): 359-380. <http://eudml.org/doc/249460>.

@article{Voskresenskaya2005,
abstract = {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 $ \eta -$products). This problem is open.We find metacyclic groups with such property and describe the Sylow $p$-subgroups, $ p \ne 2,$ for such groups. We also give a review of the results about the connection between multiplicative $\eta $-products and elements of finite orders in $SL(5,\mathbb\{C\}).$},
affiliation = {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},
author = {Voskresenskaya, Galina Valentinovna},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
number = {1},
pages = {359-380},
publisher = {Université Bordeaux 1},
title = {Multiplicative Dedekind $\eta $-function and representations of finite groups},
url = {http://eudml.org/doc/249460},
volume = {17},
year = {2005},
}

TY - JOUR
AU - Voskresenskaya, Galina Valentinovna
TI - Multiplicative Dedekind $\eta $-function and representations of finite groups
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2005
PB - Université Bordeaux 1
VL - 17
IS - 1
SP - 359
EP - 380
AB - 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 $ \eta -$products). This problem is open.We find metacyclic groups with such property and describe the Sylow $p$-subgroups, $ p \ne 2,$ for such groups. We also give a review of the results about the connection between multiplicative $\eta $-products and elements of finite orders in $SL(5,\mathbb{C}).$
LA - eng
UR - http://eudml.org/doc/249460
ER -

References

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