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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2026. Vol 56

On the Number of Real Roots of a System of Trancendental Equations in a Given Domain

Author(s)

Alexander M. Kytmanov, Olga V. Khodos

Siberian Federal University, Krasnoyarsk, Russian Federation

Abstract
The paper is devoted to the study of the number of real roots of general systems of transcendental equations with real Taylor coefficients in some domain 𝐷 of multidimensional real space. For a given entire function 𝜙 we introduce the notion of a resultant 𝑅𝜙 constructed by the power sums of the roots of the system in the negative degree and the Taylor coefficients of the function 𝜙. For such power sums we obtain formulas for their computation by means of residue integrals. It is shown that if the resultant 𝑅𝜙 has simple roots, then the number of real roots of the system in 𝐷 coincides with the number of real roots of the resultant 𝑅𝜙 in some interval.
About the Authors

Alexander M. Kytmanov, Dr. Sci. (Phys.-Math.), Prof., Siberian Federal University, Krasnoyarsk, 660041, Russian Federation, akytmanov@sfu-kras.ru 

Olga V. Khodos, Cand. Sci. (Phys.-Math.), Assoc. Prof., Siberian Federal University, Krasnoyarsk, 660041, Russian Federation, khodos olga@mail.ru

For citation
Kytmanov A. M., Khodos O. V. On the Number of Real Roots of a System of Trancendental Equations in a Given Domain. The Bulletin of Irkutsk State University. Series Mathematics, 2026, vol. 56, pp. 64–80. (in Russian) https://doi.org/10.26516/1997-7670.2026.56.64
Keywords
system of transcendental equations, resultant, simple roots, residue integrals.
UDC
517.55
MSC
32A05, 32A15, 32A27
DOI
https://doi.org/10.26516/1997-7670.2026.56.64
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