Representation of moduli spaces of curves and calculation of extremal polynomials
Sbornik. Mathematics, Tome 194 (2003) no. 4, pp. 469-494
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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.
@article{SM_2003_194_4_a0,
author = {A. B. Bogatyrev},
title = {Representation of moduli spaces of curves and calculation of extremal polynomials},
journal = {Sbornik. Mathematics},
pages = {469--494},
publisher = {mathdoc},
volume = {194},
number = {4},
year = {2003},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2003_194_4_a0/}
}
A. B. Bogatyrev. Representation of moduli spaces of curves and calculation of extremal polynomials. Sbornik. Mathematics, Tome 194 (2003) no. 4, pp. 469-494. http://geodesic.mathdoc.fr/item/SM_2003_194_4_a0/