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

Publication Info. Cambridge : Cambridge University Press, 2012.
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Online eBook via EBSCO. Access restricted to current Rider University students, faculty, and staff.
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Description 1 online resource (146 pages).
text file
Series London Mathematical Society Lecture Note Series ; no. 396
London Mathematical Society lecture note series ; no. 396.
Note Title from publishers bibliographic system (viewed 15 Feb 2012).
Summary A complete and accessible introduction to the study of arithmetic differential operators over the p-adic integers.
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.
6 A general view of arithmetic differential operators6.1 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 operators10 Some differences between arithmetic differential operators over Zp and Zurp; References; Index.
Bibliography Includes bibliographical references (pages 135-137) and index.
Local Note eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America
Language English.
Subject Differential operators.
Differential operators.
Arithmetic functions.
Arithmetic functions.
p-adic numbers.
p-adic numbers.
Genre/Form Electronic books.
Electronic books.
Added Author Ralph, Claire C.
Simanca, S. R. (Santiago R.)
Other Form: Print version: 9781107674141
ISBN 9781139084666 (ebook)
1139084666 (ebook)
9781107674141 (paperback)
110767414X (paperback)
9781107096219
1107096219
9781107089945 (electronic book)
1107089948 (electronic book)
1299707351
9781299707351
9781107101821 (e-book)
1107101824 (e-book)

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