Criteria for Algebraicity of Analytic Functions-Reference-Cited by-同舟云学术

Criteria for Algebraicity of Analytic Functions

Published:2019-10-24 Issue:5 Volume:2021 Page:3314-3330
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Bochnak Jacek¹,Gwoździewicz Janusz²,Kucharz Wojciech³

Affiliation:

1. Le Pont de l’Etang 8, 1323 Romainmôtier, Switzerland

2. Institute of Mathematics, Pedagogical University of Cracow, Podchora¸żych 2, PL-30-084 Kraków, Poland

3. Institute of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland

Abstract

Abstract We consider functions defined on an open subset of a nonsingular, either real or complex, algebraic set. We give criteria for an analytic function to be a Nash (resp. regular, resp. polynomial) function. Our criteria depend only on the behavior of such a function along irreducible nonsingular algebraic curves passing through a given point. In the proofs we use results on algebraicity of formal power series, which are also established in this paper.

Funder

National Science Center

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2021/5/3314/36583900/rnz222.pdf

Reference18 articles.

1. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge;Bochnak,1998

2. Checking real analyticity on surfaces;Bochnak;J. Math. Pures Appl. (9),2019

3. Global variants of Hartogs’ theorem;Bochnak;Arch. Math. (Basel),2019

4. Graduate Texts in Mathematics;Hirsch,1976

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A Bochnak–Siciak theorem for Nash functions over real closed fields;Israel Journal of Mathematics;2022-12-27

2. Hartogs-type theorems in real algebraic geometry, I;Journal für die reine und angewandte Mathematik (Crelles Journal);2022-07-29

3. Algebraic surfaces determine analyticity of functions;Archiv der Mathematik;2021-11-25