¹Siberian Federal University, Krasnoyarsk, Russian Federation

The work is devoted to the study of the number of real roots of systems of transcendental equations in C ⁿ with real coefficients, consisting of entire functions, in some bounded multidimensional domain D ⊂ R ⁿ . It is assumed that the number of roots of the system is discrete (then it is no more than countable). For some entire function φ(z), z ∈ C ⁿ , with real Taylor coefficients at z = 0, and a given system of equations, the concept of a resultant R_φ(t) is introduced, which is an entire function of one complex variable t. It is constructed using power sums of the roots of the system in a negative degree, found using residue integrals. If the resultant has no multiple zeros, then it is shown that the number of real roots of the system in D = {x ∈ R ⁿ : a < φ(x) < b} (x = Re z) is equal to the number of real zeros of this resultant in the interval (a, b). An example is given for a system of equations.

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

Kytmanov A. M., Khodos O. V. On Real Roots of Systems of Trancendental Equations with Real Coefficients. The Bulletin of Irkutsk State University. Series Mathematics, 2024, vol. 49, pp. 90–104. (in Russian)

https://doi.org/10.26516/1997-7670.2024.49.90

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