English

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