Arithmetic differential operators over the padic integers
 Responsibility
 Claire C. Ralph, Santiago R. Simanca.
 Language
 English.
 Imprint
 Cambridge, UK ; New York : Cambridge University Press, 2012.
 Physical description
 vi, 139 p. : ill ; 23 cm.
 Series
 London Mathematical Society lecture note series ; 396.
Access
Creators/Contributors
 Author/Creator
 Ralph, Claire C.
 Contributor
 Simanca, S. R. (Santiago R.)
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 135137) and index.
 Contents

 1. Introduction 2. The padic numbers Q_p 3. Some classical analysis on Q_p 4. Analytic functions on Z_p 5. Arithmetic differential operators on Z_p 6. A general view of arithmetic differential operators 7. Analyticity of arithmetic differential operators 8. Characteristic functions: standard padic coordinates 9. Characteristic functions: harmonic arithmetic coordinates 10. Differences between arithmetic differential operators over Z_p and Z_p^{unr} References.
 (source: Nielsen Book Data)
 Publisher's Summary
 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 padic numbers and some of the classical differential analysis on the field of padic 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 padic integers and their behaviour over the unramified completion, and a discussion of the relationship between characteristic functions of padic discs and arithmetic differential operators that disappears as soon as a single root of unity is adjoined to the padic integers. This book is essential reading for researchers and graduate students who want a first introduction to arithmetic differential operators over the padic integers.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2012
 Series
 London Mathematical Society lecture note series ; 396
 ISBN
 9781107674141 (pbk.)
 110767414X (pbk.)