Russian Mathematics

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

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

Article
  • 5 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 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    van der Waerden, B. L. Algebra (Springer-Verlag, Berlin–Heidelberg–New York, 1966; Nauka, Moscow, 1976).MATHGoogle Scholar
  2. 2.
    Kurosh, A. G. Course in Higher Algebra (Nauka, Moscow, 1968) [Russian translation].MATHGoogle 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).MathSciNetCrossRefMATHGoogle 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).MathSciNetMATHGoogle 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).MathSciNetCrossRefMATHGoogle 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).MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Gustafsson, B., Tkachev, V. G. “The Resultant on Compact Riemann Surfaces”, Comm. Math. Physics 10, 265–308 (2009).MathSciNetMATHGoogle Scholar
  9. 9.
    Morozov, A. Yu., Shakirov, Sh. R. “New and Old Resultant in Resultant Theory”, Theor. math. phys. 163 (2), 587–617 (2010).CrossRefMATHGoogle Scholar
  10. 10.
    Bykov, V. I., Tsybenova, S. B. Nonlinear Models of Chemical Kinetics (KRASAND, Moscow, 2011) [in Russian].MATHGoogle 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).CrossRefMATHGoogle 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).MathSciNetCrossRefMATHGoogle 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].MATHGoogle 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].MATHGoogle Scholar

Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Siberian Federal UniversityKrasnoyarskRussia

Personalised recommendations