Braid monodromy for a trinomial algebraic equation by means of Mellin-Barnes 
integral representations

Kocar, Mutlu; Tanabé, Susumu

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Braid monodromy for a trinomial algebraic equation by means of Mellin-Barnes integral representations

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Tanabé, Susumu
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.48550/arXiv.2409.16459
(Preprint)

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2409.16459.pdf
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Citation

Kocar, M., & Tanabé, S. (submitted). Braid monodromy for a trinomial algebraic equation by means of Mellin-Barnes integral representations.

Cite as: https://hdl.handle.net/21.11116/0000-000F-E5EC-5

Abstract

We establish a braid monodromy representation of functions satisfying an algebraic equation containing three terms (trinomial equation). We follow global analytic continuation of the roots to a trinomial algebraic equation that are expressed by Mellin-Barnes integral representations. We depict braids that arise from the monodromy around all branching points. The global braid monodromy is described in terms of rational twists of strands that yield a classical Artin braid representation of algebraic functions. As a corollary, we get a precise description of the Galois group of a trinomial algebraic equation.