02403nam a22003858a 4500001001600000003000700016005001700023006001900040007001500059008004100074020002600115020003000141040002400171050002200195082001300217100003100230245010400261260005200365264005200417300005900469336002600528337002600554338003600580490006300616500007300679520099900752650002701751650002501778650001901803700003501822776003501857786001401892830006401906856004701970CR9781139084666UkCbUP20160624102302.0m|||||o||d||||||||cr||||||||||||110506s2012||||enk s ||1 0|eng|d a9781139084666 (ebook) z9781107674141 (paperback) aUkCbUPcUkCbUPerda00aQA241 b.R25 201200an/a2n/a1 aRalph, Claire C.,eauthor.10aArithmetic Differential Operators over the p-adic Integers /cClaire C. Ralph, Santiago R. Simanca. 1aCambridge :bCambridge University Press,c2012. 1aCambridge :bCambridge University Press,c2012. a1 online resource (146 pages) :bdigital, PDF file(s). atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier0 aLondon Mathematical Society Lecture Note Series ;vno. 396 aTitle from publisher's bibliographic system (viewed on 16 Oct 2015). aThe 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 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 p-adic integers and their behaviour over the unramified completion, and a discussion of the relationship between characteristic functions of p-adic discs and arithmetic differential operators that disappears as soon as a single root of unity is adjoined to the p-adic integers. This book is essential reading for researchers and graduate students who want a first introduction to arithmetic differential operators over the p-adic integers. 0aDifferential operators 0aArithmetic functions 0ap-adic numbers1 aSimanca, Santiago R.,eauthor.08iPrint version: z9781107674141 dCambridge 0aLondon Mathematical Society Lecture Note Series ;vno. 396.40uhttp://dx.doi.org/10.1017/CBO9781139084666