Arithmetic differential equations in several variables
type: Item
instance of: scholarly article
title: Arithmetic differential equations in several variables
zbMATH Open document ID: 1198.12003
author: Alexandru Buium
author: Santiago R. Simanca
publication date: 2010-04-06T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/10468
review text: 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)].
reviewed by: Noriko Yui
Mathematics Subject Classification ID: 12H20
Mathematics Subject Classification ID: 14G20
Mathematics Subject Classification ID: 35G20
Mathematics Subject Classification ID: 11F03
Mathematics Subject Classification ID: 11G07
zbMATH DE Number: 5689403
zbMATH Keywords: arithmetic differential equations
zbMATH Keywords: elliptic curves
zbMATH Keywords: p-adic numbers
zbMATH Keywords: modular forms
MaRDI profile type: Publication
OpenAlex ID: W2487498822
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DOI: 10.5802/AIF.2504
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 5689403