Abstract:
In this paper, we describe properties of the Dedekind eta-function, constructions arising from it, and their applications in various topics of the number theory and algebra. We discuss connections with the group representation theory and the study of the structure of spaces of modular forms. The special attention is paid to the special class of modular forms, namely, eta-functions with multiplicative coefficients.
Citation:
G. V. Voskresenskaya, “Dedekind eta-function in modern research”, Proceedings of the Seminar on algebra and geometry of the Samara University, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 136, VINITI, Moscow, 2017, 103–137; J. Math. Sci. (N. Y.), 235:6 (2018), 788–833
\Bibitem{Vos17}
\by G.~V.~Voskresenskaya
\paper Dedekind eta-function in modern research
\inbook Proceedings of the Seminar on algebra and geometry of the Samara University
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 136
\pages 103--137
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into201}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3808189}
\zmath{https://zbmath.org/?q=an:07001315}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 235
\issue 6
\pages 788--833
\crossref{https://doi.org/10.1007/s10958-018-4093-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85055739078}
Linking options:
https://www.mathnet.ru/eng/into201
https://www.mathnet.ru/eng/into/v136/p103
This publication is cited in the following 4 articles:
Jing-Jun Yu, “New Congruences for Broken $k$-Diamond and $k$ Dots Bracelet Partitions”, Math. Notes, 112:3 (2022), 393–405
G. V. Voskresenskaya, “O prirode dopolnitelnogo prostranstva pri rassechenii prostranstv parabolicheskikh form”, Vestn. SamU. Estestvennonauchn. ser., 27:4 (2021), 7–13
G. V. Voskresenskaya, “Exact Cutting in Spaces of Cusp Forms with Characters”, Math. Notes, 103:6 (2018), 881–891
G. V. Voskresenskaya, “Funktsii MakKeya v prostranstvakh vysshikh urovnei”, Vestn. SamU. Estestvennonauchn. ser., 24:4 (2018), 13–18
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