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Mat. Sb., 2012, Volume 203, Number 12, Pages 35–56 (Mi msb8087)  

This article is cited in 12 scientific papers (total in 12 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.

DOI: https://doi.org/10.4213/sm8087

Full text: PDF file (636 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 517.542+517.545
MSC: Primary 14H42, 30A24, 30A28; Secondary 14H15
Received: 22.11.2011

Citation: A. B. Bogatyrev, “Conformal mapping of rectangular heptagons”, Mat. Sb., 203:12 (2012), 35–56; Sb. Math., 203:12 (2012), 1715–1735

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. A. Grigor'ev, “Numerical-analytical method for conformal mapping of polygons with six right angles”, Comput. Math. Math. Phys., 53:10 (2013), 1447–1456  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. O. A. Grigorev, N. V. Klyushnev, “Primenenie chislenno-analiticheskogo metoda konformnogo otobrazheniya dlya postroeniya setki v orebrennom kanale”, Vychislitelnye metody i programmirovanie: novye vychislitelnye tekhnologii, 15:3 (2014), 487–498  mathnet  elib
    3. S. I. Bezrodnykh, V. I. Vlasov, “Singular Riemann–Hilbert problem in complex-shaped domains”, Comput. Math. Math. Phys., 54:12 (2014), 1826–1875  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. A. B. Bogatyrev, “Image of Abel–Jacobi map for hyperelliptic genus 3 and 4 curves”, J. Approx. Theory, 191 (2015), 38–45  crossref  mathscinet  zmath  isi  elib  scopus
    5. S. I. Bezrodnykh, “Analytic continuation of the Appell function $F_1$ and integration of the associated system of equations in the logarithmic case”, Comput. Math. Math. Phys., 57:4 (2017), 559–589  mathnet  crossref  crossref  mathscinet  isi  elib
    6. A. B. Bogatyrev, O. A. Grigoriev, “Closed Formula for the Capacity of Several Aligned Segments”, Proc. Steklov Inst. Math., 298 (2017), 60–67  mathnet  crossref  crossref  isi  elib
    7. A. B. Bogatyrev, S. A. Goreinov, S. Yu. Lyamaev, “Analytical approach to multiband filter synthesis and comparison to other approaches”, Problems Inform. Transmission, 53:3 (2017), 260–273  mathnet  crossref  isi  elib
    8. A. B. Bogatyrev, S. A. Goreinov, S. Yu. Lyamaev, “Efficient synthesis of optimal multiband filter”, Russian J. Numer. Anal. Math. Modelling, 32:4 (2017), 217–223  crossref  mathscinet  zmath  isi  scopus
    9. Bogatyrev A.B. Grigor'ev O.A., “Conformal Mapping of Rectangular Heptagons II”, Comput. Methods Funct. Theory, 18:2 (2018), 221–238  crossref  mathscinet  zmath  isi  scopus
    10. S. I. Bezrodnykh, “The Lauricella hypergeometric function $F_D^{(N)}$, the Riemann–Hilbert problem, and some applications”, Russian Math. Surveys, 73:6 (2018), 941–1031  mathnet  crossref  crossref  adsnasa  isi  elib
    11. Bezrodnykh S., Bogatyrev A., Goreinov S., Grigor'ev O., Hakula H., Vuorinen M., “On Capacity Computation For Symmetric Polygonal Condensers”, J. Comput. Appl. Math., 361 (2019), 271–282  crossref  isi
    12. T. Ayano, V. M. Buchstaber, “Ultraelliptic integrals and two-dimensional sigma-functions”, Funct. Anal. Appl., 53:3 (2019), 157–173  mathnet  crossref  crossref  mathscinet  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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