Mellin transform for monomial functions of the solution to the general polynomial system
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 2, pp. 150-156.

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In the present paper we give the calculation of Mellin transform for the monomial function of the vector-solution to the general polynomial system. We essentially use linearization of the system. In scalar case it defines bijective change of variables. In case of the system of equations we weaken requirements on the mapping given by the linearization: it is proper and its degree is equal to one.
Keywords: Mellin transform
Mots-clés : algebraic equation.
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Irina A. Antipova; Tatyana V. Zykova. Mellin transform for monomial functions of the solution to the general polynomial system. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 2, pp. 150-156. http://geodesic.mathdoc.fr/item/JSFU_2013_6_2_a1/

[1] H. R. Mellin, “Résolution de l'équation algébrique générale à l'aide de la fonction gamma”, C. R. Acad. Sci. Paris Sér. I Math., 172 (1921), 658–661 | Zbl

[2] A. Yu. Semusheva, A. K. Tsikh, “Continuation of Mellin's Studies on Solving Algebraic Equation”, Complex Analysis and Differential operators, On the Occasion of the 150th Anniversary of S. V. Kovalevskaya, Krasnoyarsk, 2000, 134–146 (in Russian)

[3] E. N. Mikhalkin, “On solving general algebraic equations by integrals of elementary functions”, Sib. Math. J., 47:2 (2006), 365–371 | DOI | MR | Zbl

[4] I. A. Antipova, A. K. Tsikh, “The discriminant locus of a system of $n$ Laurent polynomials in $n$ variables”, Izv. RAN. Ser. Math., 76:5 (2012), 29–56 | DOI | Zbl

[5] I. A. Antipova, “Inversion of many-dimensional Mellin transforms and solutions of algebraic equations”, Matem. Sb., 198:4 (2007), 3–20 | DOI | MR | Zbl

[6] I. A. Antipova, “An expression for the superposition of general algebraic functions in terms of hypergeometric series”, Sib. Math. J., 44:5 (2003), 972–980 | DOI | MR | Zbl

[7] V. A. Stepanenko, “On the solution of the system of $n$ algebraic equations in $n$ unknown variables in terms of hypergeometrical functions”, Vestnik Krasnoyarskogo gosuniversiteta. Seriya phis.-mat. nauki, 2003, no. 2, 35–48 (in Russian)

[8] B. A. Dubrovin, S. P. Novikov, A. T. Fomenko, Modern Geometry. Methods and Applications, Part 2, GTM, 104, Springer-Verlag, 1985 | MR | Zbl

[9] I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, Boston, MA, 1994 | MR | Zbl