Arithmetic Differential Operators over the p-adic Integers /
Arithmetic Differential Operators over the p-adic Integers /
Claire C. Ralph, Santiago R. Simanca.
- Cambridge : Cambridge University Press, 2012.
- 1 online resource (146 pages)
- London Mathematical Society Lecture Note Series ; no. 396 .
- London Mathematical Society lecture note series ; no. 396. .
Title from publishers bibliographic system (viewed 15 Feb 2012).
Includes bibliographical references (pages 135-137) and index.
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. 9.2 Analytic functions and arithmetic differential operators10 Some differences between arithmetic differential operators over Zp and Zurp; References; Index.
A complete and accessible introduction to the study of arithmetic differential operators over the p-adic integers.
English.
9781139084666 1139084666 9781107674141 110767414X 9781107096219 1107096219 9781107089945 1107089948 1299707351 9781299707351 9781107101821 1107101824
Differential operators.
Arithmetic functions.
p-adic numbers.
Opérateurs différentiels.
Fonctions arithmétiques.
Nombres p-adiques.
MATHEMATICS--Functional Analysis.
Funciones aritméticas
Análisis p-adico
Arithmetic functions
Differential operators
p-adic numbers
Differentialoperator
p-adische Zahl
QA241 .R25 2012
512.74
Title from publishers bibliographic system (viewed 15 Feb 2012).
Includes bibliographical references (pages 135-137) and index.
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. 9.2 Analytic functions and arithmetic differential operators10 Some differences between arithmetic differential operators over Zp and Zurp; References; Index.
A complete and accessible introduction to the study of arithmetic differential operators over the p-adic integers.
English.
9781139084666 1139084666 9781107674141 110767414X 9781107096219 1107096219 9781107089945 1107089948 1299707351 9781299707351 9781107101821 1107101824
Differential operators.
Arithmetic functions.
p-adic numbers.
Opérateurs différentiels.
Fonctions arithmétiques.
Nombres p-adiques.
MATHEMATICS--Functional Analysis.
Funciones aritméticas
Análisis p-adico
Arithmetic functions
Differential operators
p-adic numbers
Differentialoperator
p-adische Zahl
QA241 .R25 2012
512.74