Geodesic
Residue integrals and Waring formulas for algebraical and transcendental systems of equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2019), pp. 40-55

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We discuss a system of algebraical and transcendental systems of equations of general form. We determine residue integrals over the cycles, connected with the system. We give formulas for their calculation and give multi-dimensional analogs of Waring formulas, i. e., connection between the coefficients of equations with power sums of the roots of system.
Keywords: algebraical and non-algebraical system of equations, residue integral, Waring formula, power sum of roots. 
@article{IVM_2019_5_a3,
     author = {A. M. Kytmanov and E. K. Myshkina},
     title = {Residue integrals and {Waring} formulas for algebraical and transcendental systems of equations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {40--55},
     publisher = {mathdoc},
     number = {5},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_5_a3/}
}
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A. M. Kytmanov; E. K. Myshkina. Residue integrals and Waring formulas for algebraical and transcendental systems of equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2019), pp. 40-55. http://geodesic.mathdoc.fr/item/IVM_2019_5_a3/