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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 404, Pages 5–17 (Mi znsl5257)  
On interaction of symplectic and orthogonal Hecke–Shimura rings of one-class quadratic forms

A. N. Andrianov

St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, St. Petersburg, Russia
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Abstract: Transformation formulas of theta-series with harmonic polynomials of one-class quadratic forms under Hecke operators are interpreted as a result of interaction of standard representation of symplectic Hecke–Shimura ring on theta-series with natural representation of orthogonal Hecke–Shimura ring on the same theta-series considered as invariants of quadratic forms. Properties of the interaction maps and their relations with action of Hecke operators are considered.
Key words and phrases: Hecke–Shimura rings, Hecke operators, interaction mappings, interaction sums, modular forms, theta-series of integral quadratic forms.
Received: 10.06.2012
English version:
Journal of Mathematical Sciences (New York), 2013, Volume 193, Issue 1, Pages 1–7
DOI: https://doi.org/10.1007/s10958-013-1428-0
Bibliographic databases:
Document Type: Article
UDC: 511
Language: English
Citation: A. N. Andrianov, “On interaction of symplectic and orthogonal Hecke–Shimura rings of one-class quadratic forms”, Analytical theory of numbers and theory of functions. Part 27, Zap. Nauchn. Sem. POMI, 404, POMI, St. Petersburg, 2012, 5–17; J. Math. Sci. (N. Y.), 193:1 (2013), 1–7
Citation in format AMSBIB
\Bibitem{And12}
\by A.~N.~Andrianov
\paper On interaction of symplectic and orthogonal Hecke--Shimura rings of one-class quadratic forms
\inbook Analytical theory of numbers and theory of functions. Part~27
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 404
\pages 5--17
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5257}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3029590}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 193
\issue 1
\pages 1--7
\crossref{https://doi.org/10.1007/s10958-013-1428-0}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84880240841}
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