Abstract
We introduce the concept of zeta-function for a system of meromorphic functions f = (f 1,..., f n) in ℂn. Using residue theory, we give an integral representation for the zeta-function which enables us to construct an analytic continuation of the zeta-function.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 5, pp. 1073–1082, September–October, 2007.
Original Russian Text Copyright © 2007 Kytmanov A. M. and Myslivets S. G.
The first author was supported by the Russian Foundation for Basic Research (Grant 05-01-00517); the second author was supported by the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-1212.2003.1).
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Kytmanov, A.M., Myslivets, S.G. On the zeta-function of systems of nonlinear equations. Sib Math J 48, 863–870 (2007). https://doi.org/10.1007/s11202-007-0088-z
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DOI: https://doi.org/10.1007/s11202-007-0088-z