On étudie une famille de formes modulaires qui sont des produits de fonctions de Dedekind. On s’intéresse aussi aux liens entre ces fonctions et les représentations des groupes finis.
In this article we consider one special class of modular forms which are products of Dedekind -functions and the relationships between these functions and representations of finite groups.
@article{JTNB_1999__11_1_247_0, author = {Voskresenskaya, Galina Valentinovna}, title = {One special class of modular forms and group representations}, journal = {Journal de Th\'eorie des Nombres de Bordeaux}, pages = {247--262}, publisher = {Universit\'e Bordeaux I}, volume = {11}, number = {1}, year = {1999}, zbl = {0954.11014}, mrnumber = {1730443}, language = {en}, url = {http://www.numdam.org/item/JTNB_1999__11_1_247_0/} }
TY - JOUR AU - Voskresenskaya, Galina Valentinovna TI - One special class of modular forms and group representations JO - Journal de Théorie des Nombres de Bordeaux PY - 1999 DA - 1999/// SP - 247 EP - 262 VL - 11 IS - 1 PB - Université Bordeaux I UR - http://www.numdam.org/item/JTNB_1999__11_1_247_0/ UR - https://zbmath.org/?q=an%3A0954.11014 UR - https://www.ams.org/mathscinet-getitem?mr=1730443 LA - en ID - JTNB_1999__11_1_247_0 ER -
Voskresenskaya, Galina V. One special class of modular forms and group representations. Journal de Théorie des Nombres de Bordeaux, Tome 11 (1999) no. 1, pp. 247-262. http://www.numdam.org/item/JTNB_1999__11_1_247_0/
[1] M24 and certain automorphic forms. Contemp. Math. 45 (1985), 223-244. | MR 822240 | Zbl 0578.10029
,[2] Finite groups and Hecke operators. Math.Ann. 283 (1989), 381-409. | MR 985239 | Zbl 0636.10021
,[3] Multiplicative products of η-functions. Contemp. Math. 45 (1985), 89-98. | Zbl 0578.10028
, , ,[4] Theory of automorphic forms of weight 1. Adv. Stud. Pure Math. 13 (1988), 503-584. | MR 971528 | Zbl 0658.10031
,[5] Higher reciprocity law, modular forms of weight 1 and elliptic curves. Nagoya Math.J. 98 (1985), 109-115. | MR 792775 | Zbl 0569.12007
,[6] On McKay's conjecture. Nagoya Math.J. 95 (1984), 85-89. | MR 759465 | Zbl 0548.10018
,[7] Courbes modulaires de gendre 1. Bull. Soc. Math. France 43 (1975), 80 pp. | Numdam | MR 417060 | Zbl 0322.14011
,[8] Affine systems of roots and the Dedekind η-function. Sb. Perev. Mat. 16 (1972), 3-49. | Zbl 0253.17009
,[9] Generators and relations for discrete groups. Second edition, Band 14 Springer-Verlag, Berlin-Göttingen- New York 1965 ix+161 pp. | MR 174618 | Zbl 0133.28002
, ,[10] 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 314766 | Zbl 0221.10029
,[11] Examples of multiplicative η- products. Sci. Pap. Coll. Arts and Sci. Univ. Tokyo. 35 (1986), 133-149. | Zbl 0597.10025
,[12] Modular forms and group representations. Matem. Zametki 52 (1992), 25-31. | MR 1187709 | Zbl 0771.11022
,[13] Cusp forms and finite subgroups in SL(5, C). Fun. anal. and appl. 29 (1995), 71-73. | MR 1340307 | Zbl 0847.11022
,[14] Modular forms and regular representations of groups of order 24. Matem. Zametki 60 (1996), 292-294. | MR 1429128 | Zbl 0923.11069
,[15] Modular forms and the representations of dihedral groups. Matem. Zametki 63 (1998), 130-133. | MR 1631789 | Zbl 0923.11070
,[16] Hypercomplex numbers, root systems and modular forms, "Arithmetic and geometry of varieties" . Samara, (1992), 48-59. | MR 1265721 | Zbl 0798.11011
,