Diagonals of the laurent series of rational functions

被引：0

作者：

D. Yu. Pochekutov

机构：

[1] Siberian Federal University,

来源：

Siberian Mathematical Journal | 2009年 / 50卷

关键词：

diagonal; Laurent series; hyperplane amoeba; separating cycle; local residue; integral representation; algebraic function;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：1081 / 1091

页数：10

共 12 条

[1]

Furstenberg H.(1967)Algebraic functions over finite fields J. Algebra 7 271-277

[2]

Denef J.(1987)Algebraic power series and diagonals J. Number Theory 26 46-67

[3]

Lipshitz L.(1989)D-finite power series J. Algebra 122 353-373

[4]

Lipshitz L.(1978)A property of the Taylor expansion of a class of rational functions in several variables J. Math. Anal. Appl. 66 679-685

[5]

Djokovič D. Ž.(2000)Laurent determinants and arrangements of hyperplane amoebas Adv. Math. 151 45-70

[6]

Forsberg M.(1967)On entire functions of exponential type and indicators of analytic functionals Acta Math. 117 1-35

[7]

Passare M.(2008)Multidimensional versions of Poincaré’s theorem for difference equations Sb.: Math. 199 1505-1521

[8]

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[9]

Kiselman C. O.(undefined)undefined undefined undefined undefined-undefined

[10]

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