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On rational functions of first-class complexity

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Abstract

It is proved that, for every rational function of two variables P(x, y) of analytic complexity one, there is either a representation of the form f(a(x) + b(y)) or a representation of the form f(a(x)b(y)), where f(x), a(x), b(x) are nonconstant rational functions of a single variable. Here, if P(x, y) is a polynomial, then f(x), a(x), and b(x) are nonconstant polynomials of a single variable.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia

    M. Stepanova

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  1. M. Stepanova
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Correspondence to M. Stepanova.

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Stepanova, M. On rational functions of first-class complexity. Russ. J. Math. Phys. 23, 251–256 (2016). https://doi.org/10.1134/S1061920816020102

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  • DOI: https://doi.org/10.1134/S1061920816020102

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