One special class of modular forms and group representations
Journal de théorie des nombres de Bordeaux, Volume 11 (1999) no. 1, pp. 247-262

In this article we consider one special class of modular forms which are products of Dedekind η-functions and the relationships between these functions and representations of finite groups.

On étudie une famille de formes modulaires qui sont des produits de fonctions η de Dedekind. On s’intéresse aussi aux liens entre ces fonctions et les représentations des groupes finis.

Galina V. Voskresenskaya. One special class of modular forms and group representations. Journal de théorie des nombres de Bordeaux, Volume 11 (1999) no. 1, pp. 247-262. doi: 10.5802/jtnb.249
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[1] G. Mason, M24 and certain automorphic forms. Contemp. Math. 45 (1985), 223-244. | MR | Zbl

[2] G. Mason, Finite groups and Hecke operators. Math.Ann. 283 (1989), 381-409. | MR | Zbl

[3] D. Dummit, H. Kisilevsky, J. Mckay, Multiplicative products of η-functions. Contemp. Math. 45 (1985), 89-98. | Zbl

[4] T. Hiramatsu, Theory of automorphic forms of weight 1. Adv. Stud. Pure Math. 13 (1988), 503-584. | MR | Zbl

[5] M. Koike, Higher reciprocity law, modular forms of weight 1 and elliptic curves. Nagoya Math.J. 98 (1985), 109-115. | MR | Zbl

[6] M. Koike, On McKay's conjecture. Nagoya Math.J. 95 (1984), 85-89. | MR | Zbl

[7] G. Ligozat, Courbes modulaires de gendre 1. Bull. Soc. Math. France 43 (1975), 80 pp. | Numdam | MR | Zbl

[8] I.G. Macdonald, Affine systems of roots and the Dedekind η-function. Sb. Perev. Mat. 16 (1972), 3-49. | Zbl

[9] H.S.M. Coxeter, W.O.J. Mozer, Generators and relations for discrete groups. Second edition, Band 14 Springer-Verlag, Berlin-Göttingen- New York 1965 ix+161 pp. | MR | Zbl

[10] G. Shimura, An introduction to the arithmetic theory of automorphic functions. Kanô Memorial Lectures, No. 1. Publications of the Mathematical Society of Japan, No. 11. Iwanami Shoten, Publishers, Tokyo; Princeton University Press, Princeton, N.J., 1971. xiv+267 pp. | MR | Zbl

[11] T. Kondo, Examples of multiplicative η- products. Sci. Pap. Coll. Arts and Sci. Univ. Tokyo. 35 (1986), 133-149. | Zbl

[12] G.V. Voskresenskaya, Modular forms and group representations. Matem. Zametki 52 (1992), 25-31. | MR | Zbl

[13] G.V. Voskresenskaya, Cusp forms and finite subgroups in SL(5, C). Fun. anal. and appl. 29 (1995), 71-73. | MR | Zbl

[14] G.V. Voskresenskaya, Modular forms and regular representations of groups of order 24. Matem. Zametki 60 (1996), 292-294. | MR | Zbl

[15] G.V. Voskresenskaya, Modular forms and the representations of dihedral groups. Matem. Zametki 63 (1998), 130-133. | MR | Zbl

[16] G.V. Voskresenskaya, Hypercomplex numbers, root systems and modular forms, "Arithmetic and geometry of varieties" . Samara, (1992), 48-59. | MR | Zbl

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