01.01.06 (Mathematical logic, algebra, and number theory)
Birth date:
18.05.1966
E-mail:
Keywords:
modular forms,
group representations,
algebraic number theory,
algebraic groups.
Subject:
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.
Biography
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.
G. V. Voskresenskaya, “On group characterization by numbers of conjugate classes”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 28:3-4 (2022), 18–25
2021
2.
G. V. Voskresenskaya, “On the nature of additional space at cutting of spaces of cusp forms”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 27:4 (2021), 7–13
2018
3.
G. V. Voskresenskaya, “Exact Cutting in Spaces of Cusp Forms with Characters”, Mat. Zametki, 103:6 (2018), 818–830; Math. Notes, 103:6 (2018), 881–891
G. V. Voskresenskaya, “Dedekind eta-function in modern research”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 136 (2017), 103–137; J. Math. Sci. (N. Y.), 235:6 (2018), 788–833
G. V. Voskresenskaya, “Cusp forms with characters of the level $\mathrm{p}$”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 2016, no. 1-2, 18–26
2015
9.
G. V. Voskresenskaya, “On representation of modular forms as homogeneous polynomials”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2015, no. 6(128), 40–49
G. V. Voskresenskaya, “On spaces of modular forms of even weight”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2014, no. 10(121), 38–47
G. V. Voskresenskaya, “The structure of modular form: the phenomen of the section”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2013, no. 6(107), 5–12
12.
G. V. Voskresenskaya, “Dedekind's eta-function in algebra and number theory: old and new problems”, Zap. Nauchn. Sem. POMI, 414 (2013), 7–30; J. Math. Sci. (N. Y.), 199:3 (2014), 248–260
2012
13.
G. V. Voskresenskaya, “The spaces that contain multiplicative eta-functions”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2012, no. 6(97), 5–12
G. V. Voskresenskaya, “The Mасkay's funсtions and elementary abelian 2-groups”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2011, no. 5(86), 18–28
2010
15.
G. V. Voskresenskaya, “Arithmetic properties of Shimura sums related to several modular forms”, Fundam. Prikl. Mat., 16:6 (2010), 7–22; J. Math. Sci., 182:4 (2012), 444–455
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
G. V. Voskresenskaya, “Finite simple groups and multiplicative $\eta$-products”, Zap. Nauchn. Sem. POMI, 375 (2010), 71–91; J. Math. Sci. (N. Y.), 171:3 (2010), 344–356
G. V. Voskresenskaya, “Sets of modular forms which define groups”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2009, no. 6(72), 21–34
2005
19.
G. V. Voskresenskaya, “Group Extensions and Hall Polynomials”, Mat. Zametki, 78:2 (2005), 180–185; Math. Notes, 78:2 (2005), 164–169
2004
20.
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
G. V. Voskresenskaya, “Multiplicative Products of Dedekind $\eta$-Functions and Group Representations”, Mat. Zametki, 73:4 (2003), 511–526; Math. Notes, 73:4 (2003), 482–495
G. V. Voskresenskaya, “Modular forms and regular representations of groups of order 24”, Mat. Zametki, 60:2 (1996), 292–294; Math. Notes, 60:2 (1996), 216–218
G. V. Voskresenskaya, “Cusp Forms and Finite Subgroups in $SL(5,\mathbb{C})$”, Funktsional. Anal. i Prilozhen., 29:2 (1995), 71–73; Funct. Anal. Appl., 29:2 (1995), 129–130
О числе классов сопряженных элементов G. V. Voskresenskaya VI Workshop and Conference on Lie Algebras, Algebraic Groups, and Invariant Theory January 31, 2017 17:40
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