Voskresenskaya, Galina Valentinovna

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Total publications: 24
Scientific articles: 24
Presentations: 1

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Associate professor
Doctor of physico-mathematical sciences (2010)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
Birth date: 18.05.1966
Keywords: modular forms, group representations, algebraic number theory, algebraic groups.


I have studied one special class of modular forms which we can define by the conditions: elements of this class are cusp forms of integer weight with characters, they are eigenforms of all Hecke operators and have no zeros outside of the cusps. The full list of these functions was obtained. They are products of Dedekind $/eta$-functions. We shall call them multiplicative $/eta$-functions. The arithmetic interpretation for the Fourier coefficients of some of these forms by Hurwitz quartenions and Cayley algebra was found. The expression of Ramanujan characters by Weil characters for some of these cusp forms was obtained. One can associate a product of $/eta$-functions with an element of finite order in a group by a linear representation. The problem of finding all finite groups such that all modular forms associated with elements of these groups by means of some faithful representations are multiplicative $/eta$-products was considered. All groups of order 24, finite subgroups in SL(5,C), metacyclic, in particular dihedral, groups were investigated. It was proved that there is no such solvable group that one can assign with all its elements by an exact representation all multiplicative $/eta$-products and only them. The coefficients of these functions were studied as central functions on a group. Also elliptic curves over finite fields were studied : graphs of 2 isogenies were constructed; the formula connecting the number of elliptic curves with the fixed group of $F_q$ rational points and the number of classes of equivalence of positive definite quadratic forms of two variables was found.


Graduated from Faculty of Mathematics and Mechanics of Samara State University in 1988 (department of algebra and geometry ). Ph.D. thesis was defended in 1993. doctor in mathematics 2010

Main publications:
  • Voskresenskaya G. V. One special class of modular forms and group representations // Journal de Thoer.des Nombres Bordeaux, 1999, 11, 247–262.
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List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. G. V. Voskresenskaya, “Exact Cutting in Spaces of Cusp Forms with Characters”, Mat. Zametki, 103:6 (2018),  818–830  mathnet  elib; Math. Notes, 103:6 (2018), 881–891  isi  scopus
2. G. V. Voskresenskaya, “MacKay functions in spaces of higher levels”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 24:4 (2018),  13–18  mathnet  elib
3. G. V. Voskresenskaya, “Dedekind eta-function in modern research”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 136 (2017),  103–137  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 235:6 (2018), 788–833  scopus
4. G. V. Voskresenskaya, “Mackay functions and exact cutting in spaces of modular forms”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 2017, 2,  15–25  mathnet  elib
5. G. V. Voskresenskaya, “Decomposition of Spaces of Modular Forms”, Mat. Zametki, 99:6 (2016),  867–877  mathnet  mathscinet  elib; Math. Notes, 99:6 (2016), 851–860  isi  scopus
6. G. V. Voskresenskaya, “Cusp forms with characters of the level $\mathrm{p}$”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 2016, 1-2,  18–26  mathnet  elib
7. G. V. Voskresenskaya, “On representation of modular forms as homogeneous polynomials”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2015, 6(128),  40–49  mathnet  elib
8. G. V. Voskresenskaya, “On spaces of modular forms of even weight”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2014, 10(121),  38–47  mathnet
9. G. V. Voskresenskaya, “The structure of modular form: the phenomen of the section”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2013, 6(107),  5–12  mathnet
10. G. V. Voskresenskaya, “Dedekind's eta-function in algebra and number theory: old and new problems”, Zap. Nauchn. Sem. POMI, 414 (2013),  7–30  mathnet; J. Math. Sci. (N. Y.), 199:3 (2014), 248–260  scopus
11. G. V. Voskresenskaya, “The spaces that contain multiplicative eta-functions”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2012, 6(97),  5–12  mathnet
12. G. V. Voskresenskaya, “The Mkay's funtions and elementary abelian 2-groups”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2011, 5(86),  18–28  mathnet
13. G. V. Voskresenskaya, “Arithmetic properties of Shimura sums related to several modular forms”, Fundam. Prikl. Mat., 16:6 (2010),  7–22  mathnet  mathscinet; J. Math. Sci., 182:4 (2012), 444–455  scopus
14. G. V. Voskresenskaya, “Finite Groups and Families of Modular Forms Associated with Them”, Mat. Zametki, 87:4 (2010),  528–541  mathnet  mathscinet  zmath; Math. Notes, 87:4 (2010), 497–509  isi  scopus
15. G. V. Voskresenskaya, “Finite simple groups and multiplicative $\eta$-products”, Zap. Nauchn. Sem. POMI, 375 (2010),  71–91  mathnet; J. Math. Sci. (N. Y.), 171:3 (2010), 344–356  scopus
16. G. V. Voskresenskaya, “Sets of modular forms which define groups”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2009, 6(72),  21–34  mathnet
17. G. V. Voskresenskaya, “Group Extensions and Hall Polynomials”, Mat. Zametki, 78:2 (2005),  180–185  mathnet  mathscinet  zmath  elib; Math. Notes, 78:2 (2005), 164–169  isi  scopus
18. G. V. Voskresenskaya, “On the problem of classification of finite groups associated to multiplicative $\eta$-products”, Fundam. Prikl. Mat., 10:4 (2004),  43–64  mathnet  mathscinet  zmath; J. Math. Sci., 140:2 (2007), 206–220  scopus
19. G. V. Voskresenskaya, “Multiplicative Products of Dedekind $\eta$-Functions and Group Representations”, Mat. Zametki, 73:4 (2003),  511–526  mathnet  mathscinet  zmath; Math. Notes, 73:4 (2003), 482–495  isi  scopus
20. G. V. Voskresenskaya, “Metacyclic groups and modular forms”, Mat. Zametki, 67:2 (2000),  163–173  mathnet  mathscinet  zmath; Math. Notes, 67:2 (2000), 129–137  isi
21. G. V. Voskresenskaya, “Modular forms and representations of the dihedral group”, Mat. Zametki, 63:1 (1998),  130–133  mathnet  mathscinet  zmath; Math. Notes, 63:1 (1998), 115–118  isi
22. G. V. Voskresenskaya, “Modular forms and regular representations of groups of order 24”, Mat. Zametki, 60:2 (1996),  292–294  mathnet  mathscinet  zmath; Math. Notes, 60:2 (1996), 216–218  isi
23. G. V. Voskresenskaya, “Cusp Forms and Finite Subgroups in $SL(5,\mathbb{C})$”, Funktsional. Anal. i Prilozhen., 29:2 (1995),  71–73  mathnet  mathscinet  zmath; Funct. Anal. Appl., 29:2 (1995), 129–130  isi
24. G. V. Voskresenskaya, “Modular forms and group representation”, Mat. Zametki, 52:1 (1992),  25–31  mathnet  mathscinet  zmath; Math. Notes, 52:1 (1992), 649–654  isi

Presentations in Math-Net.Ru
G. V. Voskresenskaya
VI Workshop and Conference on Lie Algebras, Algebraic Groups, and Invariant Theory
January 31, 2017 17:40

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