Arithmetic Differential Operators over the p-adic Integers
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 ar...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | E-Book Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge ; Tokyo
Cambridge University Press
26.01.2012
|
| Ausgabe: | 1 |
| Schriftenreihe: | London Mathematical Society lecture note series |
| Schlagworte: | |
| ISBN: | 110767414X, 9781107674141 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Inhaltsangabe:
- Cover -- Series Page -- Title -- Copyright -- Contents -- 1 Introduction -- 2 The p-adic numbers Qp -- 2.1 A pragmatic realization of Qp -- 2.2 The p-adic integers Zp and their field of fractions -- 2.3 The topology of Qp -- 2.4 Analytic and algebraic properties of Qp -- 2.5 (p − 1)-roots of unity in Qp -- 3 Some classical analysis on Qp -- 3.1 The Artin-Hasse exponential function -- 3.2 The completion of the algebraic closure of Qp -- 3.3 Zeta functions -- 4 Analytic functions on Zp -- 4.1 Strassmann's theorem -- 5 Arithmetic differential operators on Zp -- 5.1 Multiple primes I -- 6 A general view of arithmetic differential operators -- 6.1 Basic algebraic concepts -- 6.2 General δp-functions: arithmetic jet spaces -- 6.3 The analogue of a δp-linear operators for group schemes -- 6.4 Multiple primes II -- 7 Analyticity of arithmetic differential operators -- 8 Characteristic functions of discs in Zp: p-adic coordinates -- 8.1 Characteristic functions of discs of radii 1/p -- 8.2 Characteristic functions of discs of radii 1/pn -- 9 Characteristic functions of discs in Zp: harmonic arithmetic coordinates -- 9.1 A matrix associated to pm -- 9.2 Analytic functions and arithmetic differential operators -- 10 Some differences between arithmetic differential operators over Zp and Zurp -- References -- Index