Orders of Branch Points of Complete Diagonals for Laurent Series of Rational Functions of Two Variables

Key Points

The order of a branch point describes the structure of the complete diagonal in the Laurent series.
Key evidence indicates that branch points arise from the logarithmic Gauss mapping of polar curves.
Assessment involves analyzing rational functions of two complex variables and their Laurent expansions at the origin.
This finding highlights the algebraic nature of the complete diagonal, suggesting deeper connections in function theory.

Abstract

A rational function of two complex variables and all its Laurent expansions centered at the origin are considered. It is known that the complete diagonal of such an expansion is an algebraic function. The order of a branch point of the diagonal is described by means of the logarithmic Gauss mapping of a polar curve of the rational function.

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Cite This Study

D. Yu. Pochekutov (Mon,) studied this question.

synapsesocial.com/papers/69a75a0ec6e9836116a1f903 https://doi.org/https://doi.org/10.3103/s1066369x25700707

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