One special class of modular forms and group representations

Galina V. Voskresenskaya

Displaying similar documents to “One special class of modular forms and group representations”

Multiplicative Dedekind $η$ -function and representations of finite groups

Galina Valentinovna Voskresenskaya (2005)

Journal de Théorie des Nombres de Bordeaux

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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, $p \neq 2,$ for such groups. We also give a review of the results about the connection between multiplicative $η$ -products...

On the Dimensions of Spaces of Siegel Modular Forms of Weight One.

J.-S. Li (1996)

Geometric and functional analysis

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On the representation of a number as the sum of any number of squares, and in particular of twenty

R. Rankin (1962)

Acta Arithmetica

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Congruences between Siegel modular forms on the level of group cohomology

Karsten Buecker (1996)

Annales de l'institut Fourier

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Vector-valued Siegel modular forms may be found in certain cohomology groups with coefficients lying in an irreducible representation of the symplectic group. Using functoriality in the coefficients, we show that the components of the cohomology are independent of the weight parameter. The meaning of depends on a choice of parabolic subgroup of $G S p (4)$ , giving a particular direction in the change of weight. Our results complement those of Taylor and Tilouine-Urban for the two other possible...