On the Structure of the Littlewood Polynomials and their Zero Sets

TL;DR

This paper investigates the zero sets of Littlewood polynomials, exploring their fractal properties and developing methods for local approximation, linking them to traditional fractal objects.

Contribution

It introduces a new approach to analyze the local structure of Littlewood polynomial zero sets and connects them to classical fractal geometries.

Findings

Zero sets exhibit fractal-like local structures

Developed a method for local approximation of zero sets

Linked Littlewood polynomial zeros to traditional fractals

Abstract

In fractal geometry, the main objects of study have been geometric objects with a global dimension that need not be integer valued. More recently, locally fractal objects, ones in which the dimension is a local property rather than a global one, have become of interest. We explore one such object, the zero set of Littlewood polynomials, its connection to more traditional fractal objects, and develop a method for computing local approximations.