On a formula for calculating the resultant of two entire functions
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 1, pp. 17-22.

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

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 zeroes. By that, we propose an approach to construction of the resultant of two entire functions. We also give example illustrating the main result.
Keywords: resultant, entire function, Newton formulae.
@article{JSFU_2022_15_1_a2,
     author = {Evgeniya K. Myshkina},
     title = {On a formula for calculating the resultant of two entire functions},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {17--22},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2022_15_1_a2/}
}
TY  - JOUR
AU  - Evgeniya K. Myshkina
TI  - On a formula for calculating the resultant of two entire functions
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2022
SP  - 17
EP  - 22
VL  - 15
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2022_15_1_a2/
LA  - en
ID  - JSFU_2022_15_1_a2
ER  - 
%0 Journal Article
%A Evgeniya K. Myshkina
%T On a formula for calculating the resultant of two entire functions
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2022
%P 17-22
%V 15
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2022_15_1_a2/
%G en
%F JSFU_2022_15_1_a2
Evgeniya K. Myshkina. On a formula for calculating the resultant of two entire functions. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 1, pp. 17-22. http://geodesic.mathdoc.fr/item/JSFU_2022_15_1_a2/

[1] V.I. Bykov, A.M. Kytmanov, M.Z. Lazman, Elimination methods in polynomial computer algebra, Kluwer Academic Publishers, Dodrecht–Boston–Basel, 1998 | MR | Zbl

[2] L.A. Aizenberg, “On a formula for the generalized multidimensional logarithmic residue and the solution of systems of nonlinear equations”, Dokl. Akad. Nauk SSSR, 234:3 (1977), 505–508 | MR | Zbl

[3] A.A. Kytmanov, “On analogues of the recurrent Newton formulas”, Russ. Math., 53:10 (2009), 34–44 | DOI | MR | Zbl

[4] A.A. Kytmanov, A.M. Kytmanov, E.K. Myshkina, “Finding Residue Integrals for Systems of Non-algebraic Equations in \(\mathbb{C}^n\)”, Journal of Symbolic Computation, 66 (2015), 98–110 | DOI | MR | Zbl

[5] A.M. Kytmanov, Ya.M. Naprienko, “An approach to define the resultant of two entire functions”, Journal Complex Variables and Elliptic Equations, 62:2 (2017), 269–286 | DOI | MR | Zbl

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

[7] N. Bourbaki, Algebra II, Springer, Berlin, 2003 | Zbl

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

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

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

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

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

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

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

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

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

[18] A.M. Kytmanov, E.K. Myshkina, “On Finding the Resultant of Two Entire Functions”, Probl. Anal. Issues Anal., 9:3 (2020), 119–130 | DOI | MR | Zbl