Braid monodromy for a trinomial algebraic equation by means of Mellin-Barnes integral representations
Algebraic Geometry
2024-10-03 v1 Classical Analysis and ODEs
Complex Variables
Geometric Topology
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.
Keywords
Cite
@article{arxiv.2409.16459,
title = {Braid monodromy for a trinomial algebraic equation by means of Mellin-Barnes integral representations},
author = {Mutlu Kocar and Susumu Tanabe},
journal= {arXiv preprint arXiv:2409.16459},
year = {2024}
}
Comments
10 figure. A part of article is included into Ph.D. thesis of Mutlu Kocar submitted to Koc University 12/08/2024