Geodesic
Finite Groups and Families of Modular Forms Associated with Them
Matematičeskie zametki, Tome 87 (2010) no. 4, pp. 528-541.

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In the paper, a correspondence between finite groups and $q$-series which, under specialization, are Fourier expansions of modular forms is studied. The categories thus arising are investigated. The problem of describing groups to which $q$-series with multiplicative coefficients correspond is considered. Subgroups of this kind are contained in any group. The notion of modular analog of the genetic code of a group is introduced and studied.
Keywords: finite group, modular form, $q$-series, Hecke operator, Dedekind $\eta$-function, group representation, Sylow subgroup.
Mots-clés : multiplicative coefficient, Fourier expansion 
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G. V. Voskresenskaya. Finite Groups and Families of Modular Forms Associated with Them. Matematičeskie zametki, Tome 87 (2010) no. 4, pp. 528-541. http://geodesic.mathdoc.fr/item/MZM_2010_87_4_a5/

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