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JOURNALS // Matematicheskii Sbornik // Archive
Mat. Sb., 2012 Volume 203, Number 12, Pages 35–56 (Mi sm8087)
This article is cited in 18 papers

Conformal mapping of rectangular heptagons

A. B. Bogatyrevabc

a Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow
b Moscow Institute of Physics and Technology
c M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A new effective approach to calculating the direct and inverse conformal mapping of rectangular polygons onto a half-plane is put forward; it is based on the use of Riemann theta functions.
Bibliography: 14 titles.

Keywords: Christoffel-Schwarz integral, Riemann surface, Jacobian, Siegel space, theta functions.

UDC: 517.542+517.545

MSC: Primary 14H42, 30A24, 30A28; Secondary 14H15

Received: 22.11.2011

DOI: 10.4213/sm8087


 English version: Sbornik: Mathematics, 2012, 203:12, 1715–1735

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© Steklov Math. Inst. of RAS, 2026