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arXiv · 2409.16459

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

Mutlu Kocar·Susumu Tanabe
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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.

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Mutlu Kocar, Susumu Tanabe. 2024-09-24. Braid monodromy for a trinomial algebraic equation by means of Mellin-Barnes integral representations. https://arxiv.org/abs/2409.16459

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