Detail publikace

On moduli and arguments of roots of complex trinomials

ČERMÁK, J. FEDORKOVÁ, L. JÁNSKÝ, J.

Originální název

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

Root properties of a general complex trinomial have been explored in numerous papers. Two questions have attracted a significant attention: the relationships between the moduli of these roots and the trinomial’s entries, and the location of the roots in the complex plane. We consider several particular problems connected with these topics, and provide new insights into them. As two main results, we describe the set of all trinomials having a root with a given modulus, and derive explicit formula for calculations of the arguments of such roots. In this fashion, we obtain a comprehensive characterization of these roots. In addition, we develop a procedure enabling us to compute moduli and arguments of all roots of a general complex trinomial with arbitrary precision. This procedure is based on the derivation of a family of real transcendental equations for the roots’ moduli, and it is supported by the formula for their arguments. All our findings are compared with the existing results.

Klíčová slova

Complex trinomial, root, location, modulus, argument

Autoři

ČERMÁK, J.; FEDORKOVÁ, L.; JÁNSKÝ, J.

Vydáno

20. 11. 2024

Nakladatel

Mathematical Sciences Publishers

Místo

Los Angeles, , USA

ISSN

0030-8730

Periodikum

PACIFIC JOURNAL OF MATHEMATICS

Ročník

332

Číslo

Stát

Spojené státy americké

Strany od

Strany do

Strany počet

URL

https://msp.org/pjm/2024/332-1/pjm-v332-n1-p03-p.pdf

BibTex

@article{BUT191359,
  author="Jan {Čermák} and Lucie {Fedorková} and Jiří {Jánský}",
  title="On moduli and arguments of roots of complex trinomials",
  journal="PACIFIC JOURNAL OF MATHEMATICS",
  year="2024",
  volume="332",
  number="1",
  pages="39--67",
  doi="10.2140/pjm.2024.332.39",
  issn="0030-8730",
  url="https://msp.org/pjm/2024/332-1/pjm-v332-n1-p03-p.pdf"
}