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 Fundam. Prikl. Mat., 2004, Volume 10, Issue 4, Pages 43–64 (Mi fpm794)

On the problem of classification of finite groups associated to multiplicative $\eta$-products

G. V. Voskresenskaya

Samara State University

Abstract: In this article, we study finite groups such that the cusp forms associated to all elements of these groups by means of some faithful representation are modular forms with multiplicative Fourier coefficients from a special class. The Sylow subgroups of such groups of odd order are found. We consider such metacyclic groups. The groups of order 16 and the groups of order 32 that are metacyclic or are direct products of a group of order 16 and the cyclic group of order 2 are considered in detail.

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English version:
Journal of Mathematical Sciences (New York), 2007, 140:2, 206–220

Bibliographic databases:

UDC: 512.542+511.334

Citation: G. V. Voskresenskaya, “On the problem of classification of finite groups associated to multiplicative $\eta$-products”, Fundam. Prikl. Mat., 10:4 (2004), 43–64; J. Math. Sci., 140:2 (2007), 206–220

Citation in format AMSBIB
\Bibitem{Vos04} \by G.~V.~Voskresenskaya \paper On the problem of classification of finite groups associated to multiplicative $\eta$-products \jour Fundam. Prikl. Mat. \yr 2004 \vol 10 \issue 4 \pages 43--64 \mathnet{http://mi.mathnet.ru/fpm794} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2142508} \zmath{https://zbmath.org/?q=an:1070.11018} \transl \jour J. Math. Sci. \yr 2007 \vol 140 \issue 2 \pages 206--220 \crossref{https://doi.org/10.1007/s10958-007-0418-5} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33845760037} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. G. V. Voskresenskaya, “Semeistva modulyarnykh form, opredelyayuschie gruppu”, Vestn. SamGU. Estestvennonauchn. ser., 2009, no. 6(72), 21–34
2. G. V. Voskresenskaya, “Finite Groups and Families of Modular Forms Associated with Them”, Math. Notes, 87:4 (2010), 497–509
3. G. V. Voskresenskaya, “Finite simple groups and multiplicative $\eta$-products”, J. Math. Sci. (N. Y.), 171:3 (2010), 344–356
4. G. V. Voskresenskaya, “Arithmetic properties of Shimura sums related to several modular forms”, J. Math. Sci., 182:4 (2012), 444–455
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