On the roots of systems of transcendental equations
Problemy analiza, Tome 13 (2024) no. 1, pp. 37-49.

Voir la notice de l'article provenant de la source Math-Net.Ru

The article is devoted to investigation of simple and multiple roots of systems of transcendental equations. It is shown that the number is related to the number of real roots of the resultant of the system. Examples for systems of equations are given.
Keywords: systems of transcendental equations, resultant, simple root, multiple root.
@article{PA_2024_13_1_a2,
     author = {A. M. Kytmanov and O. V. Khodos},
     title = {On the roots of systems of transcendental equations},
     journal = {Problemy analiza},
     pages = {37--49},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PA_2024_13_1_a2/}
}
TY  - JOUR
AU  - A. M. Kytmanov
AU  - O. V. Khodos
TI  - On the roots of systems of transcendental equations
JO  - Problemy analiza
PY  - 2024
SP  - 37
EP  - 49
VL  - 13
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2024_13_1_a2/
LA  - ru
ID  - PA_2024_13_1_a2
ER  - 
%0 Journal Article
%A A. M. Kytmanov
%A O. V. Khodos
%T On the roots of systems of transcendental equations
%J Problemy analiza
%D 2024
%P 37-49
%V 13
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2024_13_1_a2/
%G ru
%F PA_2024_13_1_a2
A. M. Kytmanov; O. V. Khodos. On the roots of systems of transcendental equations. Problemy analiza, Tome 13 (2024) no. 1, pp. 37-49. http://geodesic.mathdoc.fr/item/PA_2024_13_1_a2/

[1] Dokl. Akad. Nauk SSSR, 252 (1980), 11-14 | MR | Zbl

[2] Bourbaki N., Algebra, v. 2, Hermann, Paris, 1961, 230 pp. | MR

[3] Bykov V. I., Kytmanov A.M., Lazman M. Z., Passare M., Elimination methods in polynomial computer algebra, Springer, 1998, 244 pp. | DOI | MR

[4] Bykov V. I., Tsybenova S. B., Nonlinear models of chemical kinetics, KRASAND, M., 2011, 400 pp. (in Russian)

[5] Chebotarev N. G., Collected works, v. 2, Academy of Sciences of the USSR, M.–L., 1949 (in Russian) | MR

[6] Kulikov V. R., Stepanenko V.A., “On solutions and Waring formulas for systems of $n$ algebraic equations in $n$ unknowns”, Algebra i Analiz, 26:5 (2014), 200–214 (in Russian) | DOI | MR

[7] Kurosh A.G., Course of higher algebra, Nauka, M., 1971, 430 pp. (in Russian) | MR

[8] Kytmanov A. A., Kytmanov A. M., Myshkina E. K., “Residue Integrals and Waring's Formulas for Class of Systems of Transcendental Equations in $\mathbb C^n$”, Journal of Complex variables and Elliptic Equations, 64 (2019), 93–111 | DOI | MR | Zbl

[9] Kytmanov A. M., Algebraic and transcendental systems of equations, SibFU, Krasnoyarsk, 2019, 354 pp. (in Russian)

[10] Kytmanov A. M., Khodos O. V., “On localization of the zeros of an entire function of finite order of growth”, Journal Complex Analysis and Operator Theory, 11 (2017), 393–416 | DOI | MR | Zbl

[11] Kytmanov A. M., Khodos O. V., “An Approach to the Determination of the Resultant of Two Entire Functions”, Russian Mathematics, 62:4 (2018), 42–51 | DOI | MR | Zbl

[12] Kytmanov A. M., Myshkina E. K., “Evaluation of power sums of roots for systems of non-algebraic equations in $\mathbb C^n$”, Russian Mathematics, 57:12 (2013), 31–43 | DOI | MR | Zbl

[13] Kytmanov A. M., Myshkina E. K., “On the calculation of power sums of roots of one class of systems of non-algebraic equations”, Siberian Electronic Mathematical Reports, 12 (2015), 190–209 | DOI | MR | Zbl

[14] Kytmanov A. M., Myshkina E. K., “Residue integrals and Waring formulas for algebraic and transcendent systems of equations”, Russian Mathematics, 63:6 (2019), 36–50 | DOI | MR | Zbl

[15] Kytmanov A. M., Naprienko Ya. M., “One approach to finding the resultant of two entire function”, Complex variables and elliptic equations, 62 (2017), 269–286 | DOI | MR | Zbl

[16] Markushevich A. I., Theory of analytic functions, v. 2, Nauka, M., 1986 (in Russian) | MR

[17] Passare M., Tsikh A., “Residue integrals and their Melin transforms”, Can. J. Math., 47:5 (1995), 1037–1050 | DOI | MR | Zbl

[18] Khodos O.V., “On Some Systems of Non-algebraic Equations in $\mathbb {C}^n$”, J. Sib. Fed. Univ. Mathematics $\$ Physics, 7:4 (2014), 455–465 | DOI | Zbl