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Russian Mathematics

, Volume 62, Issue 4, pp 42–51 | Cite as

An Approach to the Determination of the Resultant of Two Entire Functions

  • A. M. Kytmanov
  • O. V. Khodos
Article
  • 14 Downloads

Abstract

We calculate the sum of the values of an entire function at the zeros of the other entire function by means of the formula of logarithmic residue. As a result, we can answer the question whether these functions have common zeros or not. Thus, we developed an approach to the determination of the resultant of two entire functions.

Keywords

resultant entire function logarithmic residue 

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References

  1. 1.
    van der Waerden, B. L. Algebra (Springer-Verlag, Berlin–Heidelberg–New York, 1966; Nauka, Moscow, 1976).zbMATHGoogle Scholar
  2. 2.
    Kurosh, A. G. Course in Higher Algebra (Nauka, Moscow, 1968) [Russian translation].zbMATHGoogle Scholar
  3. 3.
    Bourbaki, N. Algebra. Polynomials and Fields, Ordered Proups (Nauka, Moscow, 1965) [Russian translation].Google Scholar
  4. 4.
    Krein, M. G., Naimark, M. A. “The Method of Symmetric and Hermitian Forms in the Theory of the Roots of Algebraic Equation”, Linear and Multilinear Algebra 10, 265–308 (1981).MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Gohberg, I. C., Heinig, G. “Resultant Matrix and its Generalization. I. Resultant Operator of Matrix Polynomial”, Acta Sci.Math. 72, 41–61 (1975).MathSciNetzbMATHGoogle Scholar
  6. 6.
    Gohberg, I. C., Heinig, G. “Resultant Matrix and its Generalization. II. Continual Analog of Resultant Matrix”, Acta Math. Acad. Sci. Hungar 28, 189–209 (1976).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Gohberg, I. C., Lerer, L. E. “Resultant Operators of a Pair of Analytic Functions”, Proc. Amer. Math. Soc. 72, No. 1, 65–73 (1978).MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Gustafsson, B., Tkachev, V. G. “The Resultant on Compact Riemann Surfaces”, Comm. Math. Physics 10, 265–308 (2009).MathSciNetzbMATHGoogle Scholar
  9. 9.
    Morozov, A. Yu., Shakirov, Sh. R. “New and Old Resultant in Resultant Theory”, Theor. math. phys. 163 (2), 587–617 (2010).CrossRefzbMATHGoogle Scholar
  10. 10.
    Bykov, V. I., Tsybenova, S. B. Nonlinear Models of Chemical Kinetics (KRASAND, Moscow, 2011) [in Russian].zbMATHGoogle Scholar
  11. 11.
    Kytmanov, A. M., Naprienko, Ya. M. “One Approach to Finding the Resultant of Two Entire Functions”, Complex analysis and elliptic equat. 62, No. 2, 269–286 (2017).CrossRefzbMATHGoogle Scholar
  12. 12.
    Kytmanov, A.M., Khodos, O. V. “On Localization of Zeros of an Entire Function of Finite Order of Growth”, Complex variables and operator theory 11, No. 2, 393–416 (2017).MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Shabat, B. V. Introduction to Complex Analysis (Nauka, Moscow, 1976), Vol. 1 [in Russian].Google Scholar
  14. 14.
    Titchmarsh, E. C. The Theory of Functions (Nauka, Moscow, 1980) [in Russian].zbMATHGoogle Scholar
  15. 15.
    Markushevitch, A. I. Theory of Analytical Functions (Nauka, Moscow, 1968), Vol. 2 [in Russian].Google Scholar
  16. 16.
    Bykov, V. I., Kytmanov, A. M., Lazman, M. Ya. The Exclusion Methods in Computer Algebra of Polynomials (Nauka, Novosibirsk, 1989) [in Russian].zbMATHGoogle Scholar

Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Siberian Federal UniversityKrasnoyarskRussia

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