The Krzy\.z Conjecture and an Entropy Conjecture
Complex Variables
2018-03-28 v1
Abstract
We show that if the minimum entropy for a polynomial with roots on the unit circle is attained by polynomials with equally spaced roots, then, under a generic hypothesis about the nature of the extremum, the Krzyz conjecture on the maximum modulus of the Taylor coefficients of a holomorphic function that maps the disk to the punctured disk is true.
Cite
@article{arxiv.1803.09718,
title = {The Krzy\.z Conjecture and an Entropy Conjecture},
author = {Jim Agler and John E. McCarthy},
journal= {arXiv preprint arXiv:1803.09718},
year = {2018}
}