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Zap. Nauchn. Sem. POMI, 2016, Volume 446, Pages 182–220 (Mi znsl6289)  

This article is cited in 1 scientific paper (total in 1 paper)

Calculating and drawing Belyi pairs

G. Shabat

Russian State University for the Humanities, Miusskaya pl., 6, 125993, Moscow

Abstract: The article contains a survey of the current state of the constructive part of the theory of dessin d'enfants. Namely, it is devoted to the actual establishing the correspondence between Belyi pairs and their combinatorial-topological representation. This correspondence is established in terms of the categorical equivalences, for which the necessary categories are introduced. Several connections with arithmetic are discussed. A section is devoted to one of the possible generalizations of the theory, in which the 3 branch points, allowed for the Belyi functions, are replaced by 4. Several direction of further research are presented.

Key words and phrases: dessins d'enfants, Belyi pairs, Riemann surfaces, absolute Galois group.

Full text: PDF file (796 kB)
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English version:
Journal of Mathematical Sciences (New York), 2017, 226:5, 667–693

Bibliographic databases:

UDC: 512.772.7
Received: 18.06.2016
Language:

Citation: G. Shabat, “Calculating and drawing Belyi pairs”, Combinatorics and graph theory. Part V, Zap. Nauchn. Sem. POMI, 446, POMI, St. Petersburg, 2016, 182–220; J. Math. Sci. (N. Y.), 226:5 (2017), 667–693

Citation in format AMSBIB
\Bibitem{Sha16}
\by G.~Shabat
\paper Calculating and drawing Belyi pairs
\inbook Combinatorics and graph theory. Part~V
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 446
\pages 182--220
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6289}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3520428}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 226
\issue 5
\pages 667--693
\crossref{https://doi.org/10.1007/s10958-017-3557-3}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85029680861}


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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. A. B. Bogatyrev, “How many Zolotarev fractions are there?”, Constr. Approx., 46:1 (2017), 37–45  crossref  mathscinet  zmath  isi  scopus
  • Записки научных семинаров ПОМИ
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