E-Book Overview
Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number theory. Chapters one through five form a homogenous subject matter suitable for a six-month or year-long course in computational number theory. The subsequent chapters deal with more miscellaneous subjects.
E-Book Content
Graduate Texts in Mathematics
193
Editorial Board S. Axler F.W. Gehring K.A. Ribet
Springer New York Berlin Heidelberg Barcelona HongKong London Milan Paris Singapore Tokyo
Graduate Texts in Mathematics
2 3 4 5 6 7 8 9 10 II
12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
TAKEUTIIZAluNG. Introductionto AxiomaticSet Theory. 2nd ed. OXTOBY. Measureand Category. 2nd ed. SCHAEFER. TopologicalVector Spaces. 2nded. Hn.TONlSTAMMBACH. A Course in Homological Algebra. 2nd ed. MAcLANE. Categories for the Working Mathematician. 2nd ed. HUGHESIPIPER. ProjectivePlanes. SERRE. A Coursein Arithmetic. TAKEUTIIZAluNG. Axiomatic Set Theory. HUMPHREYS. Introduction to Lie Algebras and Representation Theory. COHEN. A Course in Simple Homotopy Theory. CONWAY. Functionsof One Complex Variable I. 2nd ed. BEALS. AdvancedMathematicalAnalysis. ANDERSONIFULLER. Rings and Categories of Modules. 2nd ed. GOLUBITSKy/GUlLLEMlN. Stable Mappings and Their Singularities. BERBERIAN. Lecturesin Functional Analysisand OperatorTheory. WINTER. The Structureof Fields. ROSENBLATT. RandomProcesses. 2nd ed. HALMOS. MeasureTheory. HALMos. A HilbertSpace Problem Book. 2nded. HUSEMOLLER. Fibre Bundles. 3rd ed. HUMPHREYS. Linear AlgebraicGroups. BARNEslMACK. An Algebraic Introduction to Mathematical Logic. GREUB. LinearAlgebra.4th ed. HOLMES. GeometricFunctional Analysis and Its Applications. HEWITT/STROMBERG. Real and Abstract Analysis. MANEs. AlgebraicTheories. KELLEY. GeneralTopology. ZARlSKIlSAMUEL. CommutativeAlgebra. Vol.I. ZARlSKIlSAMUEL. CommutativeAlgebra. Vol.lI. JACOBSON. Lecturesin Abstract Algebra I. Basic Concepts. JACOBSON. Lecturesin Abstract Algebra II. Linear Algebra. JACOBSON. Lecturesin AbstractAlgebra III. Theoryof Fields and Galois Theory.
33 HIRsCH. Differential Topology. 34 SPITZER. Principlesof RandomWalk. 2nded. 35 ALExANDERIWERMER. Several Complex Variablesand BanachAlgebras.3rd ed. 36 KELLEy!NAMIOKA et al. Linear TopologicalSpaces. 37 MONK. Mathematical Logic. 38 GRAUERTIFRITZSCHE. Several Complex Variables. 39 ARVESON. An Invitationto C*-Algebras. 40 ICEMENY/SNELLIKNAPP. Denumerable MarkovChains. 2nd ed. 41 APosTOL. ModularFunctionsand Dirichlet Series in NumberTheory. 2nded. 42 SERRE. LinearRepresentations of Finite Groups. 43 GILLMANIJERISON. Rings of Continuous Functions. 44 KENDIG. ElementaryAlgebraicGeometry. 45 LoEVE. Probability Theory I. 4th ed. 46 LoEVE. Probability Theory II. 4th ed. 47 MOISE. GeometricTopologyin Dimensions2 and 3. 48 SACHslWu. GeneralRelativityfor Mathematicians. 49 GRUENBERGlWEIR. Linear Geometry. 2nded. 50 EDWARDS. Fermat'sLast Theorem. 51 KLINGENBERG. A Course in Differential Geometry. 52 HARTSHORNE. AlgebraicGeometry. 53 MANIN. A Course in Mathematical Logic. 54 GRAVER!WATKINS. Combinatorics with Emphasison the Theory of Graphs. 55 BROwNIPEARcy. Introductionto Operator Theory I: Elementsof Functional Analysis. 56 MAssEY. AlgebraicTopology: An Introduction. 57 CROWELLlFox. Introductionto Knot Theory. 58 KOBLITZ. p-adic Numbers,p-adic Analysis,and Zeta-Functions. 2nd ed. 59 LANG. CyclotomicFields. 60 ARNOLD. Mathematical Methodsin ClassicalMechanics. 2nd ed. 61 WHITEHEAD. Elementsof Homotopy Theory. (continued after index)
Henri Cohen
Advanced Topics in Computational Number Theory
i
Springer
Henri Cohen Universite de Bordeaux 1 Lab. Algorithmique Arithmetique Experimentale 351, cours de la Liberation 33405 Talence France Editoria