The real analog of the Jacobi inversion problem on a Riemann surface with boundary, its generalizations, and applications

E. I. Zverovich^a, O. B. Dolgopolova^a, E. A. Krushevskiĭ<sup>b

a</sup> Belarusian State University, Minsk, Belarus
^b Belarusian National Technical University, Minsk, Belarus

Abstract: Given a finite Riemann surface of genus $h\ge1$ with boundary composed of $m+1$ connected components we consider a system of $m+h$ real congruences analogous to the classical Jacobi inversion problem. We provide a solution to this system and its applications to boundary value problems.

Keywords: Riemann surface, Jacobi inversion problem, Abelian differential, Riemann conjugation problem, Hilbert problem, Riemann theta-function, double, Cauchy-type kernel.

UDC: 517.948.32+517.544

Received: 23.12.2014

DOI: 10.17377/smzh.2016.57.207

 English version: Siberian Mathematical Journal, 2016, 57:2, 242–259

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