On the Branching Geometry of Algebraic Functions
Abstract
This paper describes an algorithm for determining the branching geometry of algebraic functions. The graphs of these complex-valued functions have a complicated interweaving structure that can be described by analytic branches separated by singular points. Power expansions for the branches in discs centered at a point can be computed using the Newton Polygon method, and expansions around annular regions centered at the origin computed using a version of Laurent's Theorem applied to algebraic functions. However, neither of the methods enable a determination of the region of convergence of the power series. In this paper, a method using analytic continuation is used to determine the domain of analyticity for the branches, and the Root Test used to numerically check the results.
Keywords
Cite
@article{arxiv.1901.03996,
title = {On the Branching Geometry of Algebraic Functions},
author = {Dominic C. Milioto},
journal= {arXiv preprint arXiv:1901.03996},
year = {2019}
}
Comments
19 pages, 9 figures. Updated 07/12/19 to include Root Test confirmation of branching domains and corrections to text and bibliography