DOI: 10.1515/ms-2026-0358 ISSN: 0139-9918

A note on multiplicative roots of multivariable formal power series

Piotr Maćkowiak, Motaz Mokatren
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Abstract

Suppose that we are given a formal power series of many variables with coefficients in

R $\mathbb{R}$
(or
C $\mathbb{C}$
) and we wish to compute its n -th (multiplicative) root. As expected the coefficients of the root must satisfy a system of infinitely many equations. We present such a system of equations that strictly corresponds with the system for n -th root of a formal power series of one variable. Through an illustrative example, we demonstrate that the case of formal power series of many variables differs significantly from the one-variable case with respect to the existence of roots.

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