Arithmetic differential equations in several variables
This paper surveys the basic ideas, results and applications of the theory of arithmetic ordinary differential equations, based on the already published articles, e.g., [\textit{A. Buium}, Arithmetic Differential Equations. Mathematical Surveys and Monographs 118. Providence, RI: American Mathematical Society (AMS) (2005; Zbl 1088.14001)]. The paper also gives a brief survey on generalizations of some of these ideas to arithmetic partial differential equations, based on papers recently published, e.g., \textit{Arithmetic partial differential equations, I, II}, by the authors [Adv. Math. 225, No. 2, 689--793 (2010; Zbl 1217.12005), Adv. Math. 225, No. 3, 1308--1340 (2010; Zbl 1234.12006)].
scientific article; zbMATH DE number 5689403
scientific article