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Matematicheskie Zametki, 2010, Volume 87, Issue 4, Pages 528–541
DOI: https://doi.org/10.4213/mzm6323 (Mi mzm6323) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Finite Groups and Families of Modular Forms Associated with Them

G. V. Voskresenskaya

Samara State University
Full-text PDF (522 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm6323
Abstract: 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, multiplicative coefficient, Fourier expansion, Hecke operator, Dedekind η-function, group representation, Sylow subgroup.
Received: 22.09.2008
Revised: 03.11.2009
English version:
Mathematical Notes, 2010, Volume 87, Issue 4, Pages 497–509
DOI: https://doi.org/10.1134/S0001434610030284
Bibliographic databases:
Document Type: Article
UDC: 511.2+511.334
Language: Russian
Citation: G. V. Voskresenskaya, “Finite Groups and Families of Modular Forms Associated with Them”, Mat. Zametki, 87:4 (2010), 528–541; Math. Notes, 87:4 (2010), 497–509
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm6323
  • https://www.mathnet.ru/eng/mzm/v87/i4/p528
    • This publication is cited in the following 2 articles:
    1. G. V. Voskresenskaya, “Dedekind eta-function in modern research”, J. Math. Sci. (N. Y.), 235:6 (2018), 788–833  mathnet  mathnet  crossref  scopus
    2. G. V. Voskresenskaya, “Dedekind's eta-function in algebra and number theory: old and new problems”, J. Math. Sci. (N. Y.), 199:3 (2014), 248–260  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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