On Z2 harmonic functions on $\mathbb{R}^2$ and the polynomial Pell's equation

TL;DR

This paper investigates Z2 harmonic functions with point singularities on the plane, exploring their properties and solutions related to the polynomial Pell's equation, contributing to the understanding of harmonic analysis and algebraic equations.

Contribution

It introduces a novel analysis of Z2 harmonic functions with singularities on ^2 and connects these functions to solutions of the polynomial Pell's equation.

Findings

Characterization of Z2 harmonic functions with singularities

Connection between harmonic functions and Pell's equation solutions

Insights into the structure of differential forms and spinors

Abstract

There has been many studies on Z2 harmonic functions, differential forms or spinors recently. This paper focuses on a very special and relatively simple aspect: Z2 harmonic functions on $\mathbb{R}^2$ with point singularities.