2022
DOI: 10.1007/s40840-021-01230-8
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Zeros of a Family of Complex-Valued Harmonic Trinomials

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Cited by 4 publications
(6 citation statements)
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“…Recently, the corresponding geometric sectors as in (II) for harmonic trinomials of the form (1.2) with A = 1, B ∈ C \ {0}, C = −1 has been derived in [22]. For references about location, counting, geometry, and lower/uppers bounds for the moduli of roots for harmonic polynomials including probabilistic approaches and numerical experiments, we refer to [1,11,12,13,22,23,24,25,26,27,29,30,31,32,36,37,38,39,40,54,55,56] and the references therein.…”
mentioning
confidence: 99%
“…Recently, the corresponding geometric sectors as in (II) for harmonic trinomials of the form (1.2) with A = 1, B ∈ C \ {0}, C = −1 has been derived in [22]. For references about location, counting, geometry, and lower/uppers bounds for the moduli of roots for harmonic polynomials including probabilistic approaches and numerical experiments, we refer to [1,11,12,13,22,23,24,25,26,27,29,30,31,32,36,37,38,39,40,54,55,56] and the references therein.…”
mentioning
confidence: 99%
“…More specifically, the sign of the order of a zero or a pole depends on whether it is in the sense-preserving region (positive order) or the sense-reversing region (negative order). See [11] for a more detailed discussion of why this convention makes sense. For this paper, we take the following to be our definitions of the order of a zero and the order of a pole.…”
Section: Definitions and Toolsmentioning
confidence: 99%
“…They have sought to determine the maximum and minimum number of zeros, how the number of zeros varies with the coefficients, and the location of these zeros. See [7][8][9][10][11][12][13][14][15]. We discuss several of their results in some detail because they are the motivation for the current work.…”
Section: Introductionmentioning
confidence: 99%
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