LEADER 03856nam 22007332 450 001 9910810153203321 005 20151005020621.0 010 $a1-139-88774-2 010 $a1-139-08466-6 010 $a1-107-08994-8 010 $a1-107-10182-4 010 $a1-107-09621-9 010 $a1-107-10420-3 010 $a1-107-09312-0 035 $a(CKB)2550000001095239 035 $a(EBL)891271 035 $a(OCoLC)793359427 035 $a(SSID)ssj0000683488 035 $a(PQKBManifestationID)11930582 035 $a(PQKBTitleCode)TC0000683488 035 $a(PQKBWorkID)10688993 035 $a(PQKB)11601575 035 $a(UkCbUP)CR9781139084666 035 $a(Au-PeEL)EBL891271 035 $a(CaPaEBR)ebr10718031 035 $a(CaONFJC)MIL501986 035 $a(MiAaPQ)EBC891271 035 $a(PPN)261286455 035 $a(EXLCZ)992550000001095239 100 $a20110506d2012|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aArithmetic differential operators over the p-adic integers /$fClaire C. Ralph, Santiago R. Simanca$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2012. 215 $a1 online resource (vi, 139 pages) $cdigital, PDF file(s) 225 1 $aLondon Mathematical Society lecture note series ;$v396 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a1-107-67414-X 311 $a1-299-70735-1 320 $aIncludes bibliographical references (p. 135-137) and index. 327 $aThe p-adic numbers Qp -- Some classical analysis on Qp -- The Artin-Hasse exponential function -- The completion of the algebraic closure of Qp -- Zeta functions -- Analytic functions on Zp -- Arithmetic differential operators on Zp -- A general view of arithmetic differential operators -- Analyticity of arithmetic differential operators -- Characteristic functions of discs in Zp: p-adic coordinates -- Characteristic functions of discs in Zp: harmonic coordinates -- Some differences between (Se(B-operators over Zp and Zur p. 330 $aThe study of arithmetic differential operators is a novel and promising area of mathematics. This complete introduction to the subject starts with the basics: a discussion of p-adic numbers and some of the classical differential analysis on the field of p-adic numbers leading to the definition of arithmetic differential operators on this field. Buium's theory of arithmetic jet spaces is then developed succinctly in order to define arithmetic operators in general. Features of the book include a comparison of the behaviour of these operators over the p-adic integers and their behaviour over the unramified completion, and a discussion of the relationship between characteristic functions of p-adic discs and arithmetic differential operators that disappears as soon as a single root of unity is adjoined to the p-adic integers. This book is essential reading for researchers and graduate students who want a first introduction to arithmetic differential operators over the p-adic integers. 410 0$aLondon Mathematical Society lecture note series ;$v396. 606 $aDifferential operators 606 $aArithmetic functions 606 $ap-adic numbers 615 0$aDifferential operators. 615 0$aArithmetic functions. 615 0$ap-adic numbers. 676 $a515.7242 686 $aMAT 123f$2stub 686 $aSI 320$2rvk 686 $aSK 540$2rvk 700 $aRalph$b Claire C.$0477392 702 $aSimanca$b S. R$g(Santiago R.), 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910810153203321 996 $aArithmetic differential operators over the p-adic integers$9239905 997 $aUNINA