Arithmetic Differential Operators over the padic Integers
$62.00 USD
Part of London Mathematical Society Lecture Note Series
 Authors:
 Claire C. Ralph, Cornell University, New York
 Santiago R. Simanca, Université de Nantes, France
 Date Published: June 2013
 availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
 format: Adobe eBook Reader
 isbn: 9781139382649
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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.
Read more The first introductory book on the subject
 Accessible to those with a grasp of algebraic number theory
 Allows those without a strong training in commutative algebra and algebraic geometry to achieve a deep understanding of the subject
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×Product details
 Date Published: June 2013
 format: Adobe eBook Reader
 isbn: 9781139382649
 availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of 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}
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