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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Partially supported by National Science Foundation Grant DMS 1665260.
Partially supported by National Science Foundation Grant DMS 1565243.
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Agler, J., McCarthy, J.E. The Krzyż Conjecture and an Entropy Conjecture. JAMA 144, 207–226 (2021). https://doi.org/10.1007/s11854-021-0178-z
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DOI: https://doi.org/10.1007/s11854-021-0178-z