The Krzyż Conjecture and an Entropy Conjecture

Jim Agler; John E. McCarthy

doi:10.1007/s11854-021-0178-z

The Krzyż Conjecture and an Entropy Conjecture

Jim Agler
, John E. McCarthy

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	207-226
Number of pages	20
Journal	Journal d'Analyse Mathematique
Volume	144
Issue number	1
DOIs	https://doi.org/10.1007/s11854-021-0178-z
State	Published - Dec 2021

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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.",

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AB - 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.

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The Krzyż Conjecture and an Entropy Conjecture

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