Univalent functions with half-integral coefficients

TL;DR

This paper classifies univalent functions with half-integral Taylor coefficients, identifying twelve such functions beyond the nine with integral coefficients, and explores their geometric properties.

Contribution

It extends Friedman's classification from integral to half-integral coefficients, revealing twelve additional univalent functions and analyzing their geometric features.

Findings

Identified twelve univalent functions with half-integral coefficients

Extended Friedman's classification from integral to half-integral coefficients

Analyzed geometric properties of the twelve functions

Abstract

B. Friedman found in his 1946 paper that the set of analytic univalent functions on the unit disk in the complex plane with integral Taylor coefficients consists of nine functions. In the present paper, we prove that the similar set obtained by replacing "integral" by "half-integral" consists of another twelve functions in addition to the nine. We also observe geometric properties of the twelve functions.