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＜E-Book＞
Arithmetic Differential Operators over the p-adic Integers / Claire C. Ralph, Santiago R. Simanca
(London Mathematical Society Lecture Note Series ; 396)

Publisher	Cambridge : Cambridge University Press
Year	2012
Size	1 online resource (146 pages) : digital, PDF file(s)
Authors	*Ralph, Claire C. author Simanca, Santiago R. author
Subjects	LCSH:Differential operators LCSH:Arithmetic functions LCSH:p-adic numbers
Notes	Title from publisher's bibliographic system (viewed on 11 Nov 2016) The study of arithmetic differential operators is a novel and promising area of mathematics. This complete introduction to the subject starts with the basics: a discussion of p-adic numbers and some of the classical differential analysis on the field of p-adic numbers leading to the definition of arithmetic differential operators on this field. Buium's theory of arithmetic jet spaces is then developed succinctly in order to define arithmetic operators in general. Features of the book include a comparison of the behaviour of these operators over the p-adic integers and their behaviour over the unramified completion, and a discussion of the relationship between characteristic functions of p-adic discs and arithmetic differential operators that disappears as soon as a single root of unity is adjoined to the p-adic integers. This book is essential reading for researchers and graduate students who want a first introduction to arithmetic differential operators over the p-adic integers HTTP:URL=http://dx.doi.org/10.1017/CBO9781139084666

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