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ČERMÁK, J. FEDORKOVÁ, L. KUREŠ, M.
Original Title
Complete classification scheme for the distribution of trinomial zeros with respect to their moduli
Type
journal article in Web of Science
Language
English
Original Abstract
The paper discusses the location of zeros of a real trinomial with respect to their moduli. Although this problem was solved in classical and modern literature, a complete answer to the problem is still missing. Without loss of generality, we consider the unitary modulus and derive a comprehensive classification scheme representing a one-to-one correspondence between given configurations of zeros and appropriate parts of the parameter space. Doing this, explicit formulae for the numbers of zeros with a modulus greater than, equal to, or less than 1 are presented. Conversely, for prescribed counts of such zeros, appropriate regions in the parameter space are described analytically. Also, basic properties of these regions are discussed, including implicit and parametric forms of curves separating these regions.As a basic proof technique, the D-partition method is used and supported by analytical tools, and by an extended version of a classical result from the elementary number theory. The derived classification results are illustrated by several examples and comparisons with the existing results.
Keywords
real trinomial; zero; location; modulus; difference equation; asymptotic behaviour
Authors
ČERMÁK, J.; FEDORKOVÁ, L.; KUREŠ, M.
Released
1. 8. 2022
Publisher
KOSSUTH LAJOS TUDOMANYEGYETEM
Location
DEBRECEN
ISBN
0033-3883
Periodical
Publicationes Mathematicae Debrecen
Year of study
101
Number
1-2
State
Hungary
Pages from
119
Pages to
146
Pages count
28
URL
https://publi.math.unideb.hu/load_doc.php?p=4054&t=pap
BibTex
@article{BUT179901, author="Jan {Čermák} and Lucie {Fedorková} and Miroslav {Kureš}", title="Complete classification scheme for the distribution of trinomial zeros with respect to their moduli", journal="Publicationes Mathematicae Debrecen", year="2022", volume="101", number="1-2", pages="119--146", doi="10.5486/PMD.2022.9209", issn="0033-3883", url="https://publi.math.unideb.hu/load_doc.php?p=4054&t=pap" }