ArticleOriginal scientific text
Title
Diagonal series of rational functions
Authors 1, 1
Affiliations
- Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
Abstract
Some representations of Nash functions on continua in ℂ as integrals of rational functions of two complex variables are presented. As a simple consequence we get close relations between Nash functions and diagonal series of rational functions.
Bibliography
- L. Bieberbach, Analytic Extensions, Nauka, Moscow 1967 (in Russian).
- P. Deligne, Intégration sur un cycle évanescent, Invent. Math. 76 (1983), 129-143.
- J. Denef and L. Lipshitz, Algebraic power series and diagonals, J. Number Theory 26 (1987), 46-67.
- H. Furstenberg, Algebraic functions over finite fields, J. Algebra 7 (1967), 271-277.
- S. Łojasiewicz, Introduction to Complex Analytic Geometry, PWN, Warszawa 1988 (in Polish).
- K. V. Safonov, On conditions for algebraicity and rationality of the sum of a power series, Mat. Zametki 41 (3) (1987), 325-332 (in Russian).
- P. Tworzewski, Intersections of analytic sets with linear subspaces, Ann. Scuola Norm. Sup. Pisa (4) 17 (2) (1990), 227-271.