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.
@article{bwmeta1.element.bwnjournal-article-apmv55z1p57bwm, author = {S\l awomir Cynk and Piotr Tworzewski}, title = {Diagonal series of rational functions}, journal = {Annales Polonici Mathematici}, volume = {55}, year = {1991}, pages = {57-63}, zbl = {0798.32009}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv55z1p57bwm} }
Sławomir Cynk; Piotr Tworzewski. Diagonal series of rational functions. Annales Polonici Mathematici, Tome 55 (1991) pp. 57-63. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv55z1p57bwm/
[000] [1] L. Bieberbach, Analytic Extensions, Nauka, Moscow 1967 (in Russian).
[001] [2] P. Deligne, Intégration sur un cycle évanescent, Invent. Math. 76 (1983), 129-143. | Zbl 0538.13007
[002] [3] J. Denef and L. Lipshitz, Algebraic power series and diagonals, J. Number Theory 26 (1987), 46-67. | Zbl 0609.12020
[003] [4] H. Furstenberg, Algebraic functions over finite fields, J. Algebra 7 (1967), 271-277. | Zbl 0175.03903
[004] [5] S. Łojasiewicz, Introduction to Complex Analytic Geometry, PWN, Warszawa 1988 (in Polish). | Zbl 0773.32007
[005] [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). | Zbl 0622.32009
[006] [7] P. Tworzewski, Intersections of analytic sets with linear subspaces, Ann. Scuola Norm. Sup. Pisa (4) 17 (2) (1990), 227-271. | Zbl 0717.32006