FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1995, VOLUME 1, NUMBER 3, PAGES 781-799

Fields of definition of rational functions of one variable with three critical values

V.O.Filimonenkov
G.B.Shabat

Rational functions of one complex variable with three critical values are considered. According to Grothendieck theory, such functions are classified by the isotopic classes of the connected spherical graphs. By a suitable fractional-linear variable substitution these coefficients can be transformed to algebraic numbers. The paper is devoted to the problem of minimization of irrationality degrees of these coefficients.

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Last modified: October 3, 1997.