Egerváry's theorems for harmonic trinomials-Reference-Cited by-同舟云学术

Egerváry's theorems for harmonic trinomials

Published:2024-02 Issue:1 Volume:172 Page:170-186
ISSN:0236-5294
Container-title:Acta Mathematica Hungarica
language:en
Short-container-title:Acta Math. Hungar.

Author:

Barrera G.,Barrera W.,Navarrete J. P.

Abstract

AbstractWe study the arrangements of the roots in the complex plane for the lacunary harmonic polynomials called harmonic trinomials. We provide necessary and sufficient conditions so that two general harmonic trinomials have the same set of roots up to a rotation around the origin in the complex plane, a reflection over the real axis, or a composition of the previous both transformations. This extends the results of Jenő Egerváry given in [19] for the setting of trinomials to the setting of harmonic trinomials.

Publisher

Springer Science and Business Media LLC

Link

https://link.springer.com/content/pdf/10.1007/s10474-024-01403-4.pdf

Reference53 articles.

1. G. Barrera, W. Barrera and J. P. Navarrete, On the number of roots of harmonic trinomials, J. Math. Anal. Appl., 514 (2022), Paper No. 126313, 14 pp.

2. G. Barrera, W. Barrera and J. P. Navarrete, The stability region for Schur stable trinomials with general complex coefficients,arXiv:2304.09147 (2023).

3. W. Barrera, J. C. Maga˜ña and J. P. Navarrete, Trinomials, torus knots and chains,Trans. Amer. Math. Soc., 376 (2023), 2963–3004.

4. D. Belkić, All the trinomial roots, their powers and logarithms from the Lambert series, Bell polynomials and Fox–Wright function: illustration for genome multiplicity in survival of irradiated cells, J. Math. Chem., 57 (2019), 59–106.

5. P. Bohl, Zur Theorie der trinomischen Gleichungen, Math. Ann., 65 (1908), 556–566.