On finding the resultant of two entire functions
Problemy analiza, Tome 9 (2020) no. 3, pp. 119-130.

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Using Newton's recurrent formulae, we find the product of values of an entire function of one variable in zeroes of another entire function. This allows to answer whether they have common zeros. By that, we propose an approach to construction of the resultant of two entire functions. We also give examples illustrating the main result.
Keywords: resultant, entire function, Newton formulae.
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A. M. Kytmanov; E. K. Myshkina. On finding the resultant of two entire functions. Problemy analiza, Tome 9 (2020) no. 3, pp. 119-130. http://geodesic.mathdoc.fr/item/PA_2020_9_3_a7/

[1] Bourbaki N., Algebra. Polynomials and Fields, Ordered Groups, Russian translation, Nauka, M., 1965 | MR

[2] Bykov V. I., Tsybenova S. B., Nonlinear Models of Chemical Kinetics, KRASAND, M., 2011 (in Russian)

[3] Chamberlin S., Rafizadeh A., “A generalized Newton-Girard formula for monomial symmetric polynomials”, Rocky Mountain J. Math., 50:3 (2020), 941–946 | DOI | MR | Zbl

[4] Gohberg I. C., Heinig G., “Resultant Matrix and its Generalization. I. Resultant Operator of Matrix Polynomial”, Acta Sci. Math., 72 (1975), 41–61 | MR

[5] Gohberg I. C., Heinig G., “Resultant Matrix and its Generalization. II. Continual Analog of Resultant Matrix”, Acta Math. Acad. Sci. Hungar., 28 (1976), 189–209 | DOI | MR | Zbl

[6] Gohberg I. C., Lerer L. E., “Resultant Operators of a Pair of Analytic Functions”, Proc. Amer. Math. Soc., 72:1 (1978), 65–73 | DOI | MR | Zbl

[7] Gould H. W., “The Girard-Waring power sum formulas for symmetric functions and Fibonacci sequences”, Fibonacci Quart., 37:2 (1999), 135–140 | MR | Zbl

[8] Gustafsson B., Tkachev V. G., “The Resultant on Compact Riemann Surfaces”, Comm. Math. Physics., 10 (2009), 265–308 | DOI | MR

[9] Krein M. G., Naimark M. A., “The Method of Symmetric and Hermitian Forms in the Theory of the Separation of the Roots of Algebraic Equation”, Linear and Multilinear Algebra, 10:4 (1981), 265–308 | DOI | MR | Zbl

[10] Kurosh A. G., Course in Higher Algebra, Russian translation, Nauka, M., 1968 | MR

[11] Kytmanov A. M., Naprienko Ya. M., “An Approach to Define the Resultant of Two Entire Functions”, Complex variables and elliptic equat., 62:2 (2017), 269–286 | DOI | MR | Zbl

[12] Kytmanov A. M., Khodos O. V., “On Localization of Zeros of an Entire Function of Finite Order of Growth”, Complex analysis and operator theory, 11:2 (2017), 393–416 | DOI | MR | Zbl

[13] 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

[14] Kytmanov A. M., Myshkina E. K., “On Some Approach for Finding the Resultant of Two Entire Functions”, J. Siberian Federal Univ. Math. Phys., 12:4 (2019), 434–438 | DOI | MR

[15] Morozov A. Yu., Shakirov Sh. R., “New and Old Results in Resultant Theory”, Theor. math. phys., 163:2 (2010), 587–617 | DOI | Zbl

[16] van der Waerden B. L., Algebra, Springer-Verlag, Berlin–Heidelderg–New York, 1966 | MR | Zbl