Abstract
We consider the problem of the algebraicity of diagonal series for the Laurent expansions of rational functions, geometrically identifiable using the amoeba of the denominator or an integer point in its Newton polyhedron. We give sufficient conditions for the algebraicity of diagonals basing on the theory of multidimensional residues and topological properties of the complements to collections of complex hypersurfaces in complex analytic varieties.
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Original Russian Text Copyright © 2009 Pochekutov D. Yu.
The author was supported by the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh 2427.2008.01), Siberian Federal University, and the Program “Development of the Scientific Potential of Higher School” of the Russian Federal Agency for Education (Grant 2.1.1/4620).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 6, pp. 1370–1383, November–December, 2009.
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Pochekutov, D.Y. Diagonals of the laurent series of rational functions. Sib Math J 50, 1081–1091 (2009). https://doi.org/10.1007/s11202-009-0119-z
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DOI: https://doi.org/10.1007/s11202-009-0119-z