数论中的基本方法

图书标准信息

• 作者 M.B.Nathanson 著
• 出版社 世界图书出版公司
• 出版时间 2003-06
• 版次 1
• ISBN 9787506259569
• 定价 49.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 513页

【内容简介】

Thissecondeditionof"CategoriesWork"addstwonewchaptersontopicsofactiveinterest.Oneisonsymmetricmonoidalcategoriesandbraidedmonoidalcategoriesandthecoherencetheoremsforthem--itemsofinterestintheirownrightandalsoinviewoftheiruseinstringtheoryinquantumfieldtheory.Thesecondnewchapterdescribes2-categoriesandthehigher-dimensionalcategoriesthathaverecentlycomeintoprominence.Inaddition，thebibliographyhasbeenexpandedtocoversomeofthemanyotherrecentadvancesconcerningcategories.

【目录】

Preface
Notationandconventions
ⅠAFirstCourseinNumberTheory
1DivisibilityandPrimes
1.1DivisionAlgorithm
1.2GreatestCommonDivisors
1.3TheEuclideanAlgorithmandContinuedFractions
1.4TheFundamentalTheoremofArithmetic
1.5EuclidsTheoremandtheSieveofEratosthenes
1.6ALinearDiophantineEquation
1.7Notes

2Congruences
2.1TheRingofCongruenceClasses
2.2LinearCongruences
2.3TheEulerPhiFunction
2.4ChineseRemainderTheorem
2.5EulersTheoremandFermatsTheorem
2.6PseudoprimesandCarmichaelNumbers
2.7PublicKeyCryptography
2.8Notes

3PrimitiveRootsandQuadraticReciprocity
3.1PolynomialsandPrimitiveRoots
3.2PrimitiveRootstoCompositeModuli
3.3PowerResidues
3.4QuadraticResidues
3.5QuadraticReciprocityLaw
3.6QuadraticResiduestoCompositeModuli
3.7Notes

4FourierAnalysisonFiniteAbelianGroups
4.1TheStructureofFiniteAbelianGroups
4.2CharactersofFiniteAbelianGroups
4.3ElementaryFourierAnalysis
4.4PoissonSummation
4.5TraceFormulaeonFiniteAbelianGroups
4.6GaussSumsandQuadraticReciprocity
4.7TheSignoftheGaussSum
4.8Notes

5TheabcConjecture
5.1IdealsandRadicals
5.2Derivations
5.3MasonsTheorem
5.4TheabcConjecture
5.5TheCongruenceabcConjecture
5.6Notes

ⅡDivisorsandPrimesinMultiplicativeNumberTheory
6ArithmeticFunctions
6.1TheRingofArithmeticFunctions
6.2MeanValuesofArithmeticFunctions
6.3TheMSbiusFunction
6.4MultiplicativeFunctions
6.5ThemeanvalueoftheEulerPhiFunction
6.6Notes

7DivisorFunctions
7.1DivisorsandFactorizations
7.2ATheoremofRamanujan
7.3SumsofDivisors
7.4SumsandDifferencesofProducts
7.5SetsofMultiples
7.6AbundantNumbers
7.7Notes

8PrimeNumbers
8.1ChebyshevsTheorems
8.2MertenssTheorems
8.3TheNumberofPrimeDivisorsofanInteger
8.4Notes

9ThePrimeNumberTheorem
9.1GeneralizedVonMangoldtFunctions
9.2SelbergsFormulae
9.3TheElementaryProof
9.4IntegerswithkPrimeFactors
9.5Notes

10PrimesinArithmeticProgressions
10.1DirichletCharacters
10.2DirichletL-Functions
10.3PrimesModulo4
10.4TheNonvanishingofL(1,X)
10.5Notes

ⅢThreeProblemsinAdditiveNumberTheory
11WaringsProblem
11.1SumsofPowers
11.2StableBases
11.3ShnirelmansTheorem
11.4WaringsProblemforPolynomials
11.5Notes

12SumsofSequencesofPolynomials
12.1SumsandDifferencesofWeightedSets
12.2LinearandQuadraticEquations
12.3AnUpperBoundforRepresentations
12.4WaringsProblemforSequencesofPolynomials
12.5Notes
13LiouvillesIdentity
13.1AMiraculousFormula
13.2PrimeNumbersandQuadraticForms
13.3ATernaryForm
13.4ProofofLiouvillesIdentity
13.5TwoCorollaries
13.6Notes

14SumsofanEvenNumberofSquares
14.1SummaryofResults
14.2ARecursionFormula
14.3SumsofTwoSquares
14.4SumsofFourSquares
14.5SumsofSixSquares
14.6SumsofEightSquares
14.7SumsofTenSquares
14.8Notes

15PartitionAsymptotics
15.1TheSizeofp(n)
15.2PartitionFunctionsforFiniteSets
15.3UpperandLowerBoundsforlogp(n)
15.4Notes
16AnInverseTheoremforPartitions
16.1DensityDeterminesAsymptotics
16.2AsymptoticsDetermineDensity
16.3AbelianandTauberianTheorems
16.4Notes
References
Index