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The Number of Zeros in a Disk of a Complex Polynomial with Coefficients Satisfying Various Monotonicity Conditions
Version 1
: Received: 30 August 2023 / Approved: 31 August 2023 / Online: 1 September 2023 (09:07:04 CEST)
A peer-reviewed article of this Preprint also exists.
Gardner, R.; Gladin, M. The Number of Zeros in a Disk of a Complex Polynomial with Coefficients Satisfying Various Monotonicity Conditions. AppliedMath 2023, 3, 722-729. Gardner, R.; Gladin, M. The Number of Zeros in a Disk of a Complex Polynomial with Coefficients Satisfying Various Monotonicity Conditions. AppliedMath 2023, 3, 722-729.
Abstract
Motivated by results on the location of zeros of a complex polynomial with monotonicity conditions on the coefficients (such as the classical Eneström-Kakeya Theorem, and its recent generalizations), we impose similar conditions and give bounds on the number of zeros in certain regions. We do so by introducing a reversal in monotonicity conditions on the real and imaginary parts of the coefficients, and also on their moduli. The results presented naturally apply to certain classes of lacunary polynomials.
Keywords
Complex polynomials; counting zeros; monotone coefficients
Subject
Computer Science and Mathematics, Analysis
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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