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Analog of the Cauchy kernel and the Riemann boundary problem of a three-sheeted surface of genus two

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Literature cited

  1. Yu. I. Cherskii, “Conjugacy problem on two-sheeted surfaces,” Matem. Issled.,3, No. 3, Kishinev (1968).

  2. É. I. Zverovich, “The Behnke-Stein kernel and the solution in closed form of the Riemann problem on the torus,” Dokl. Akad. Nauk SSSR,188, No. 1 (1969).

  3. É. I. Zverovich, “Analog to the Cauchy kernel and the Riemann boundary problem on a hyperelliptic surface,” ibid.,192, No. 3 (1970).

  4. N. G. Chebotarev, Theory of Algebraic Functions [in Russian], Gostekhizdat, Moscow-Leningrad (1948).

    Google Scholar 

  5. G. Springer, Introduction to the Theory of Riemann Surfaces [Russian translation], Fizmatgiz, Moscow (1960).

    Google Scholar 

  6. K. Hensel and G. Landsberg, Theorie der algebraischen Funktionen einer Variablen und ihre Anwendung auf algebraischen Kurven und abelsche Integrale, Leipzig (1902).

  7. W. Koppelman, “Singular integral equations, boundary value problem, and Riemann-Roch theorem,” J. Math. Mech.,10, No. 2 (1961).

  8. É. I. Zverovich and G. S. Litvinchuk, “Boundary problems with shifts for analytic functions and singularity functional equations,” Usp.Matem. Nauk,23, No. 3 (41) (1968).

  9. A. Krazer, Lehrbuch der Thetafunktionen, Leipzig (1903).

  10. R. N. Abdulaev, “Homogeneous Riemann problem on closed Riemann surfaces,” Dokl. Akad. Nauk SSSR,160, No. 5 (1965).

  11. F. D. Gakhov, Boundary Problems [in Russian], Fizmatgiz, Moscow (1963).

    Google Scholar 

  12. F. D. Gakhov and É. G. Khasabov, “On the Hilbert boundary problem for multiply-connected regions,” in: Investigation into Modern Problems in the Theory of Functions of a Complex Variable [in Russian], Fizmatgiz, Moscow (1960).

    Google Scholar 

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Authors and Affiliations

  1. Odessa State University, USSR

    V. E. Kruglov

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  1. V. E. Kruglov
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 24, No. 3, pp. 352–364, May–June, 1972.

I should like to take this opportunity to thank Yu. I. Cherskii and É. I. Zverovich for their interest in this paper.

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Kruglov, V.E. Analog of the Cauchy kernel and the Riemann boundary problem of a three-sheeted surface of genus two. Ukr Math J 24, 287–296 (1972). https://doi.org/10.1007/BF01086240

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  • DOI: https://doi.org/10.1007/BF01086240

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