Journal of Mathematical Sciences

, Volume 78, Issue 2, pp 232–240 | Cite as

A type of automorphic form

  • N. A. Shirokov


The aim of this paper is to construct a Γ-automorphic form of weight −2k for a given finitely generated Fuchsian group Γ of the second kind. The construction heavily relies on important properties of the outer function introduced by Widom, which were established by the author. The constructed Γ-automorphic form possesses the highest possible smoothness for the weight −2k. Bibliography: 8 titles.


Automorphic Form Fuchsian Group Carleson Measure Outer Function Parabolic Element 
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Literature Cited

  1. 1.
    J. Lehner, “Discontinuous groups and automorphic functions”, in: Math. surveys, VIII, Am. Math. Soc., Providence (1964).Google Scholar
  2. 2.
    Ch. Pommerenke, “On automorphic forms and Carleson sets”,Mich. Math. J.,23, No. 2, 129–136 (1976)MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    D. Daase, “Automorphe Formen und Carleson-Mengen”,Compl. Var. Theory Appl.,2, No. 1, 51–65 (1983).MATHMathSciNetGoogle Scholar
  4. 4.
    N. A. Shirokov, “Division and multiplication by inner functions in spaces of analytic functions smooth up to the boundary”,Lecture Notes Math.,864, 413–439 (1981).MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    N. A. Shirokov, “A note on Fuchsian groups”,Zap. Nauchn. Sem. LOMI,149, 181–185 (1986).MATHGoogle Scholar
  6. 6.
    N. A. Shirokov, “Fuchsian groups with Carleson limit sets”,Funkts. Anal. Ego Prilozhen.,24, No. 4, 92–93 (1990).MATHMathSciNetGoogle Scholar
  7. 7.
    A. F. Beardon,The Geometry of Discrete Groups, Graduate Texts in Math., bf 91, Springer-Verlag, New York-Berlin (1983).MATHGoogle Scholar
  8. 8.
    J. Garnett,Bounded Analytic Functions, Academic Press, New York (1981).MATHGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • N. A. Shirokov

There are no affiliations available

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