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Mat. Sb., 2003, Volume 194, Number 4, Pages 3–28 (Mi msb725)  

This article is cited in 5 scientific papers (total in 5 papers)

Representation of moduli spaces of curves and calculation of extremal polynomials

A. B. Bogatyrev

Institute of Numerical Mathematics, Russian Academy of Sciences

Abstract: The classical Chebyshev and Zolotarev polynomials are the first ranks of the hierarchy of extremal polynomials, which are typical solutions of problems on the conditional minimization of the uniform norm over a space of polynomials. In the general case such polynomials are connected with hyperelliptic curves the genus of which labels the ranks of the hierarchy. Representations of the moduli spaces of such curves are considered in this paper with applications to the calculation of extremal polynomials. Uniformizing curves by special Schottky groups one obtains effectively computable parametric expressions for extremal polynomials in terms of linear series of Poincare.

DOI: https://doi.org/10.4213/sm725

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English version:
Sbornik: Mathematics, 2003, 194:4, 469–494

Bibliographic databases:

UDC: 517.545+517.518.826
MSC: Primary 41A50, 30F60, 32G15; Secondary 14H15, 30F40
Received: 27.06.2002

Citation: A. B. Bogatyrev, “Representation of moduli spaces of curves and calculation of extremal polynomials”, Mat. Sb., 194:4 (2003), 3–28; Sb. Math., 194:4 (2003), 469–494

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. A. B. Bogatyrev, “Combinatorial description of a moduli space of curves and of extremal polynomials”, Sb. Math., 194:10 (2003), 1451–1473  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Bogatyrev A., “Effective computation of optimal stability polynomials”, Calcolo, 41:4 (2004), 247–256  crossref  mathscinet  zmath  isi  elib
    3. A. B. Bogatyrev, “Effective solution of the problem of the optimal stability polynomial”, Sb. Math., 196:7 (2005), 959–981  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. Vilmos Totik, “Chebyshev polynomials on a system of curves”, JAMA, 118:1 (2012), 317  crossref  mathscinet  zmath  isi
    5. A. B. Bogatyrev, “Combinatorial analysis of the period mapping: the topology of 2D fibres”, Sb. Math., 210:11 (2019), 1531–1562  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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