Diagonal series of rational functions

Sławomir Cynk; Piotr Tworzewski

Annales Polonici Mathematici (1991)

  • Volume: 55, Issue: 1, page 57-63
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Sławomir Cynk, and Piotr Tworzewski. "Diagonal series of rational functions." Annales Polonici Mathematici 55.1 (1991): 57-63. <http://eudml.org/doc/262526>.

@article{SławomirCynk1991,
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.},
author = {Sławomir Cynk, Piotr Tworzewski},
journal = {Annales Polonici Mathematici},
keywords = {integral representations; diagonal series; Nash functions; rational holomorphic functions},
language = {eng},
number = {1},
pages = {57-63},
title = {Diagonal series of rational functions},
url = {http://eudml.org/doc/262526},
volume = {55},
year = {1991},
}

TY - JOUR
AU - Sławomir Cynk
AU - Piotr Tworzewski
TI - Diagonal series of rational functions
JO - Annales Polonici Mathematici
PY - 1991
VL - 55
IS - 1
SP - 57
EP - 63
AB - 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.
LA - eng
KW - integral representations; diagonal series; Nash functions; rational holomorphic functions
UR - http://eudml.org/doc/262526
ER -

References

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  1. [1] L. Bieberbach, Analytic Extensions, Nauka, Moscow 1967 (in Russian). 
  2. [2] P. Deligne, Intégration sur un cycle évanescent, Invent. Math. 76 (1983), 129-143. Zbl0538.13007
  3. [3] J. Denef and L. Lipshitz, Algebraic power series and diagonals, J. Number Theory 26 (1987), 46-67. Zbl0609.12020
  4. [4] H. Furstenberg, Algebraic functions over finite fields, J. Algebra 7 (1967), 271-277. Zbl0175.03903
  5. [5] S. Łojasiewicz, Introduction to Complex Analytic Geometry, PWN, Warszawa 1988 (in Polish). Zbl0773.32007
  6. [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). Zbl0622.32009
  7. [7] P. Tworzewski, Intersections of analytic sets with linear subspaces, Ann. Scuola Norm. Sup. Pisa (4) 17 (2) (1990), 227-271. Zbl0717.32006

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