Geodesic
On solutions and Waring's formulae for the system of $n$ algebraic equations with $n$ unknowns
Algebra i analiz, Tome 26 (2014) no. 5, pp. 200-214 
V. R. Kulikov; V. A. Stepanenko. On solutions and Waring's formulae for the system of $n$ algebraic equations with $n$ unknowns. Algebra i analiz, Tome 26 (2014) no. 5, pp. 200-214. http://geodesic.mathdoc.fr/item/AA_2014_26_5_a6/
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     title = {On solutions and {Waring's} formulae for the system of~$n$ algebraic equations with~$n$ unknowns},
     journal = {Algebra i analiz},
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     year = {2014},
     volume = {26},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2014_26_5_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

[1] Mellin Hj., “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] Zhdanov O. N., Tsikh A. K., “Issledovanie kratnykh integralov Mellina–Barnsa s pomoschyu mnogomernykh vychetov”, Sib. mat. zh., 39:2 (1988), 281–298 | MR | Zbl

[3] Horn J., “Über hypergeometrische Funktionen zweier Veränderlichen”, Math. Ann., 117 (1940), 384–414 | DOI | MR | Zbl

[4] Passare M., Tsikh A., “Algebraic equations and hypergeometric series”, The legacy of Niels Henrik Abel (Oslo, Norway, 2002), Springer-Verlag, Berlin, 2004, 653–672 | DOI | MR | Zbl

[5] Gelfand I. M., Zelevinskii A. V., Kapranov M. M., “Gipergeometricheskie funktsii i toricheskie mnogoobraziya”, Funkts. anal. i ego pril., 23:2 (1989), 12–26 | MR | Zbl

[6] Sadykov T., “On the Horn system of partial differential equations and series of hypergeometric type”, Math. Scand., 91:1 (2002), 127–149 | MR | Zbl

[7] Varchenko A., Multidimensional hypergeometric functions and the representation theory of Lie algebras and quantum groups, Adv. Ser. Math. Phys., 21, World Sci. Publ. Co., River Edge, NJ, 1995 | DOI | MR | Zbl

[8] Antipova I. A., “Obrascheniya mnogomernykh preobrazovanii Mellina i resheniya algebraicheskikh uravnenii”, Mat. sb., 198:4 (2007), 3–20 | DOI | MR | Zbl

[9] Sturmfels B., “Solving algebraic equations in terms of $A$-hypergeometric series”, Discrete Math., 210:1–3 (2000), 171–181 | DOI | MR | Zbl

[10] Semusheva A. Yu., Tsikh A. K., “Prodolzhenie issledovanii Mellina o reshenii algebraicheskikh uravnenii”, Kompleksnyi analiz i differentsialnye operatory, Sb. nauch. tr., KrasGU, Krasnoyarsk, 2000, 134–146

[11] Birkeland R., “Über die Auflösung algebraischer Gleichungen durch hypergeometrische Funktionen”, Math. Z., 26:1 (1927), 565–578 | DOI | MR

[12] Antipova I. A., Mikhalkin E. N., “Analiticheskie prodolzheniya obschei algebraicheskoi funktsii s pomoschyu ryadov Pyuizo”, Tr. Mat. in-ta RAN, 279, 2012, 9–19 | MR | Zbl

[13] Antipova I. A., “Vyrazhenie superpozitsii obschikh algebraicheskikh funktsii cherez gipergeometricheskie ryady”, Sib. mat. zh., 44:5 (2003), 972–980 | MR | Zbl

[14] Antipova I. A., Tsikh A. K., “Diskriminantnoe mnozhestvo sistemy $n$ polinomov Lorana ot $n$ peremennykh”, Izv. RAN. Ser. mat., 76:5 (2012), 29–56 | DOI | MR | Zbl

[15] Stepanenko V. A., “O reshenii sistemy $n$ algebraicheskikh uravnenii ot $n$ neizvestnykh s pomoschyu gipergeometricheskikh funktsii”, Vestn. Krasnoyarsk. gos. un-ta, 2003, no. 1, 35–48

[16] Aizenberg L. A., Yuzhakov A. P., Integralnye predstavleniya i vychety v mnogomernom kompleksnom analize, Nauka, Novosibirsk, 1979

[17] Yuzhakov A. P., “O primenenii kratnogo logarifmicheskogo vycheta dlya razlozheniya neyavnykh funktsii v stepennye ryady”, Mat. sb., 97(139):2 (1975), 177–192 | MR | Zbl

[18] Bykov V. I., Kytmanov A. M., Lazman M. Z., Metody isklyucheniya v kompyuternoi algebre mnogochlenov, Nauka, Novosibirsk, 1991 | Zbl