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Zapiski Nauchnykh Seminarov LOMI, 1983, Volume 129, Pages 17–29 (Mi znsl4254)  

This article is cited in 2 scientific papers (total in 2 papers)

On accessory coefficients of second order Fuchsian equation with real singular points

A. B. Venkov
Full-text PDF (660 kB) Citations (2)
Abstract: In the paper the author considers equations of Fuchs and Schwarz connected with a conformal mapping of the half-plane onto curvilinear polygon. The equations are studied from point of view of spectral theory of automorphic furc tions. A monodromy group is supposed to be a special Fuchsian group. The main question investigated in the paper (following Poincare) is the problem of finding the accessory coefficients as functions of singular points of Fuchsian equation. The principal results of the paper are following ones. In addition to another paper of the author “On explicit formulas for accessory coefficients in Schwarz equation”, Functional, analysis and its appl., 1983, N 2, in this paper the Fourier expansions of Siegel–Selberg series with relation to parabolic subgroups of monodromy group are studied (theorem 1). From here the author receives the formulas for all Fourier coefficients of Klein invariant (theorems 3, 4) and the formulas for singular points of Fuchs equation in geemetric terms of generating polygon (theorem 5). In conclution, the example of quadrangle is given for which the problem of funding the accessory parameters is simplified.
Bibliographic databases:
Document Type: Article
UDC: 517.862.2+517.941.6
Language: Russian
Citation: A. B. Venkov, “On accessory coefficients of second order Fuchsian equation with real singular points”, Automorphic functions and number theory. Part I, Zap. Nauchn. Sem. LOMI, 129, "Nauka", Leningrad. Otdel., Leningrad, 1983, 17–29
Citation in format AMSBIB
\Bibitem{Ven83}
\by A.~B.~Venkov
\paper On accessory coefficients of second order Fuchsian equation with real singular points
\inbook Automorphic functions and number theory. Part~I
\serial Zap. Nauchn. Sem. LOMI
\yr 1983
\vol 129
\pages 17--29
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl4254}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=703005}
\zmath{https://zbmath.org/?q=an:0516.30033}
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  • https://www.mathnet.ru/eng/znsl/v129/p17
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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