On the Laurent coefficients of the Riemann map for the complement of the Mandelbrot set

TL;DR

This paper investigates the Laurent coefficients of the Riemann map for the Mandelbrot set's complement, confirming an empirical observation and clarifying their arithmetic properties.

Contribution

It refines a previous result on the arithmetic nature of Laurent coefficients, providing a rigorous confirmation of Zagier's empirical observations.

Findings

Confirmed the arithmetic properties of Laurent coefficients

Extended previous results on conformal mappings

Validated empirical observations by Zagier

Abstract

We straighten a result of [5] about arithmetic properties of the Laurent coefficients of the conformal isomorphism from the complement of the unit disk onto the complement of the Mandelbrot set. This confirms an empirical observation by Don Zagier, see [1]