On moduli and arguments of roots of complex trinomials

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F24%3APU152718" target="_blank" >RIV/00216305:26210/24:PU152718 - isvavai.cz</a>

Výsledek na webu

<a href="https://msp.org/pjm/2024/332-1/pjm-v332-n1-p03-p.pdf" target="_blank" >https://msp.org/pjm/2024/332-1/pjm-v332-n1-p03-p.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.2140/pjm.2024.332.39" target="_blank" >10.2140/pjm.2024.332.39</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On moduli and arguments of roots of complex trinomials

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On moduli and arguments of roots of complex trinomials

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

PACIFIC JOURNAL OF MATHEMATICS

ISSN

0030-8730

e-ISSN

—

Svazek periodika

332

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

29

Strana od-do

39-67

Kód UT WoS článku

001363278100003

EID výsledku v databázi Scopus

2-s2.0-85211171904