The Krzy\.z Conjecture and an Entropy Conjecture

Jim Agler; John E. McCarthy

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arXiv · 1803.09718

The Krzy\.z Conjecture and an Entropy Conjecture

Jim Agler·John E. McCarthy

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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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Jim Agler, John E. McCarthy. 2018-03-26. The Krzy\.z Conjecture and an Entropy Conjecture. https://arxiv.org/abs/1803.09718

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