ArticleOriginal scientific text

Title

Diagonal series of rational functions

Authors 1, 1

Affiliations

  1. 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

  1. L. Bieberbach, Analytic Extensions, Nauka, Moscow 1967 (in Russian).
  2. P. Deligne, Intégration sur un cycle évanescent, Invent. Math. 76 (1983), 129-143.
  3. J. Denef and L. Lipshitz, Algebraic power series and diagonals, J. Number Theory 26 (1987), 46-67.
  4. H. Furstenberg, Algebraic functions over finite fields, J. Algebra 7 (1967), 271-277.
  5. S. Łojasiewicz, Introduction to Complex Analytic Geometry, PWN, Warszawa 1988 (in Polish).
  6. 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).
  7. P. Tworzewski, Intersections of analytic sets with linear subspaces, Ann. Scuola Norm. Sup. Pisa (4) 17 (2) (1990), 227-271.
Pages:
57-63
Main language of publication
English
Received
1990-08-27
Published
1991
Exact and natural sciences