数论中的基本方法（英文版）
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内容提要：
This second edition of "Categories Work" adds two new chapters on topics of active interest. One is on symmetric monoidal categories and braided monoidal categories and the coherence theorems for them--items of interest in their own right and also in view of their use in string theory in quantum field theory. The second new chapter describes 2-categories and the higher-dimensional categories that have recently come into prominence. In addition, the bibliography has been expanded to cover some of the many other recent advances concerning categories.
编辑推荐：
This second edition of "Categories Work" adds two new chapters on topics of active interest. One is on symmetric monoidal categories and braided monoidal categories and the coherence theorems for them--items of interest in their own right and also in view of their use in string theory in quantum field theory. The second new chapter describes 2-categories and the higher-dimensional categories that have recently come into prominence. In addition, the bibliography has been expanded to cover some of the many other recent advances concerning categories.
此书为英文版！ 目录：
Preface
Notationandconventions Ⅰ AFirstCourseinNumberTheory 1 DivisibilityandPrimes 1.1 DivisionAlgorithm 1.2 GreatestCommonDivisors 1.3 TheEuclideanAlgorithmandContinuedFractions 1.4 TheFundamentalTheoremofArithmetic 1.5 Euclid'sTheoremandtheSieveofEratosthenes 1.6 ALinearDiophantineEquation 1.7 Notes 2 Congruences 2.1 TheRingofCongruenceClasses 2.2 LinearCongruences 2.3 TheEulerPhiFunction 2.4 ChineseRemainderTheorem 2.5 Euler'sTheoremandFermat'sTheorem 2.6 PseudoprimesandCarmichaelNumbers 2.7 PublicKeyCryptography 2.8 Notes 3 PrimitiveRootsandQuadraticReciprocity 3.1 PolynomialsandPrimitiveRoots 3.2 PrimitiveRootstoCompositeModuli 3.3 PowerResidues 3.4 QuadraticResidues 3.5 QuadraticReciprocityLaw 3.6 QuadraticResiduestoCompositeModuli 3.7 Notes 4 FourierAnalysisonFiniteAbelianGroups 4.1 TheStructureofFiniteAbelianGroups 4.2 CharactersofFiniteAbelianGroups 4.3 ElementaryFourierAnalysis 4.4 PoissonSummation 4.5 TraceFormulaeonFiniteAbelianGroups 4.6 GaussSumsandQuadraticReciprocity 4.7 TheSignoftheGaussSum 4.8 Notes 5 TheabcConjecture 5.1 IdealsandRadicals 5.2 Derivations 5.3 Mason'sTheorem 5.4 TheabcConjecture 5.5 TheCongruenceabcConjecture 5.6 Notes Ⅱ DivisorsandPrimesinMultiplicativeNumberTheory 6 ArithmeticFunctions 6.1 TheRingofArithmeticFunctions 6.2 MeanValuesofArithmeticFunctions 6.3 TheMSbiusFunction 6.4 MultiplicativeFunctions 6.5 ThemeanvalueoftheEulerPhiFunction 6.6 Notes 7 DivisorFunctions 7.1 DivisorsandFactorizations 7.2 ATheoremofRamanujan 7.3 SumsofDivisors 7.4 SumsandDifferencesofProducts 7.5 SetsofMultiples 7.6 AbundantNumbers 7.7 Notes 8 PrimeNumbers 8.1 Chebyshev'sTheorems 8.2 Mertens'sTheorems 8.3 TheNumberofPrimeDivisorsofanInteger 8.4 Notes 9 ThePrimeNumberTheorem 9.1 GeneralizedVonMangoldtFunctions 9.2 Selberg'sFormulae 9.3 TheElementaryProof 9.4 IntegerswithkPrimeFactors 9.5 Notes 10 PrimesinArithmeticProgressions 10.1 DirichletCharacters 10.2 DirichletL-Functions 10.3 PrimesModulo4 10.4 TheNonvanishingofL(1,X) 10.5 Notes Ⅲ ThreeProblemsinAdditiveNumberTheory 11 Waring'sProblem 11.1 SumsofPowers 11.2 StableBases 11.3 Shnirel'man'sTheorem 11.4 Waring'sProblemforPolynomials 11.5 Notes 12 SumsofSequencesofPolynomials 12.1 SumsandDifferencesofWeightedSets 12.2 LinearandQuadraticEquations 12.3 AnUpperBoundforRepresentations 12.4 Waring'sProblemforSequencesofPolynomials 12.5 Notes 13 Liouville'sIdentity 13.1 AMiraculousFormula 13.2 PrimeNumbersandQuadraticForms 13.3 ATernaryForm 13.4 ProofofLiouville'sIdentity 13.5 TwoCorollaries 13.6 Notes 14 SumsofanEvenNumberofSquares 14.1 SummaryofResults 14.2 ARecursionFormula 14.3 SumsofTwoSquares 14.4 SumsofFourSquares 14.5 SumsofSixSquares 14.6 SumsofEightSquares 14.7 SumsofTenSquares 14.8 Notes 15 PartitionAsymptotics 15.1 TheSizeofp(n) 15.2 PartitionFunctionsforFiniteSets 15.3 UpperandLowerBoundsforlogp(n) 15.4 Notes 16 AnInverseTheoremforPartitions 16.1 DensityDeterminesAsymptotics 16.2 AsymptoticsDetermineDensity 16.3 AbelianandTauberianTheorems 16.4 Notes References Index |