Geodesic
Evaluation of power sums of roots for systems of non-algebraic equations in~$\mathbb C^n$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2013), pp. 36-50

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The goal of this paper is the evaluation of power sums of roots for systems of non-algebraic equations consisting of entire or meromorphic functions of finite order of growth. These power sums are connected with some residue integrals different from the Grothendieck residues. As an application we evaluate sums of certain multiple series.
Keywords: non-algebraic systems of equations, power sums of roots, residue integral. 
@article{IVM_2013_12_a3,
     author = {A. M. Kytmanov and E. K. Myshkina},
     title = {Evaluation of power sums of roots for systems of non-algebraic equations in~$\mathbb C^n$},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {36--50},
     publisher = {mathdoc},
     number = {12},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_12_a3/}
}
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A. M. Kytmanov; E. K. Myshkina. Evaluation of power sums of roots for systems of non-algebraic equations in~$\mathbb C^n$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2013), pp. 36-50. http://geodesic.mathdoc.fr/item/IVM_2013_12_a3/