Arithmetic Differential Operators over the p-adic Integers / Claire C. Ralph, Santiago R. Simanca.

Contributor(s):

Material type: Text

TextSeries: London Mathematical Society lecture note series ; no. 396.Publication details: Cambridge : Cambridge University Press, 2012.Description: 1 online resource (146 pages)Content type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9781139084666
1139084666
9781107674141
110767414X
9781107096219
1107096219
9781107089945
1107089948
1299707351
9781299707351
9781107101821
1107101824

Subject(s): Genre/Form:

Electronic books.

Additional physical formats: Print version:: No titleDDC classification:

512.74

LOC classification:

QA241 .R25 2012

Other classification:

MAT 123f
SI 320
SK 540
SK 620

Online resources:

Click here to access online

Contents:

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.

Summary: A complete and accessible introduction to the study of arithmetic differential operators over the p-adic integers.

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Title from publishers bibliographic system (viewed 15 Feb 2012).

A complete and accessible introduction to the study of arithmetic differential operators over the p-adic integers.

880-01 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.