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math.QA2002
Rational functions with prescribed critical points
I. Scherbak
A rational function is the ratio of two complex polynomials in one variable without common roots. Its degree is the maximum of the degrees of the numerator and the denominator. Rat…
math.QA2001
Critical points of functions, sl_2 representations, and Fuchsian differential equations with only univalued solutions
I. Scherbak, A. Varchenko
Let a second order Fuchsian differential equation with only univalued solutions have finite singular points at z_1, ..., z_n with exponents (a_1,b_1), ..., (a_n,b_n). Let the expon…