哈代数论（英文版·第6版）

图书标准信息

• 作者 哈代（G.H.Hardy）、哈代（G.H.Hardy） 著
• 出版社 人民邮电出版社
• 出版时间 2009-11
• 版次 1
• ISBN 9787115214270
• 定价 59.00元
• 装帧 平装
• 开本 32开
• 纸张 胶版纸
• 页数 621页
• 字数 576千字
• 正文语种 英语
• 丛书 图灵原版数字·统计学系列

【内容简介】

《哈代数论(英文版·第6版)》是数论领域的一部传世名著，成书于作者在牛津大学、剑桥大学等学校授课的讲义。书中从各个不同角度对数论进行了阐述，内容包括素数、无理数、同余、费马定理、连分数、不定式、二次域、算术函数、分化等。新版修订了每章末的注解，简要介绍了数论最新的发展；增加了一章讲述椭圆曲线，这是数论中最重要的突破之一。还列出进一步阅读的文献。
《哈代数论(英文版·第6版)》适合数学专业本科生、研究生和教师用作教材或参考书，也适合对数论感兴趣的专业人士阅读参考。

【作者简介】

G.H.Hardy（1877-1947），20世纪上半叶享有世界声誉的数学大师，是英国数学界和英国分析学派的领袖，对数论和分析学的发展有巨大的贡献和重大的影响，除了自己的研究工作之外，他还培养和指导了众多数学大家，包括印度数学奇才拉马努金和我国数学家华罗庚。
E.M.Wright（1906-2005），英国著名数学家，毕业于牛津大学，是G．H．Hardy的学生。生前担任英国名校阿伯丁大学校长多年。爱丁堡皇家学会会士、伦敦数学会会士。曾任JournalofGraphTheory和ZentralbtattfurMathematik的名誉主编。

【目录】

Ⅰ.THESERIESOFPRIMES(1)
1.1.Divisibilityofintegers
1.2.Primenumbers
1.3.Statementofthefundamentaltheoremofarithmetic
1.4.Thesequenceofprimes
1.5.Somequestionsconcerningprimes
1.6.Somenotations
1.7.Thelogarithmicfunction
1.8.Statementoftheprimenumbertheorem

Ⅱ.THESERIESOFPRIMES(2)
2.1.FirstproofofEuclidssecondtheorem
2.2.FurtherdeductionsfromEuclidsargument
2.3.Primesincertainarithmeticalprogressions
2.4.SecondproofofEuclidstheorem
2.5.FermatsandMersennesnumbers
2.6.ThirdproofofEuclidstheorem
2.7.Furtherresultsonformulaeforprimes
2.8.Unsolvedproblemsconcerningprimes
2.9.Moduliofintegers
2.10.Proofofthefundamentaltheoremorarithmetic
2.11.Anotherproofofthefundamentaltheorem

Ⅲ.FAREYSERIESANDATHEOREMOFMINKOWSKI
3.1.ThedefinitionandsimplestpropertiesofaFareyseries
3.2.Theequivalenceofthetwocharacteristicproperties
3.3.FirstproofofTheorems28and
3.4.Secondproofofthetheorems
3.5.Theintegrallattice
3.6.Somesimplepeopertiesofthefundamentallattice
3.7.ThirdproofofTheorems28and
3.8.TheFarevdissectionofthecontinuum
3.9.AtheoremofMinkowski
3.10ProofofMinkowskistheorem
3.11.DevelopmentsofTheorem

Ⅳ.IRRATIONALNUMBERS
4.1.Somegeneralities
4.2.Numbersknowntobeirrational
4.3.ThetheoremofPythagorasanditsgeneralizations
4.4.TheuseofthefundamentaltheoremintheproofsofTheorems43-
4.5.Ahistoricaldigression3o
4.6.Geometricalproofoftheirrationalityof√
4.7.Somemoreirrationalnumbers
Ⅴ.CONGRUENCESANDRESIDUES
5.1.Highestcommondivisorandleastcommonmultiple
5.2.Congruencesandclassesofresidues
5.3.Elementaryorooertiesofcongruences
5.4.Linearcongruences
5.5.Eulersfunctionφ(m)
5.6.AoolicationsofTheorems59and61totrigonometricalsums
5.7.Ageneralprinciple
5.8.Constructionoftheregularpolygonof17sides

Ⅵ.FFRMATsTHEOREMANDITSCONSEOUENCES
6.1.Fermatstheorem
6.2.Somepropertiesofbinomialcoefficients
6.3.AsecondproofofTheorem
6.4.ProofofTheorem
6.5.Quadraticresidues
6.6.SoecialcasesofTheorem79：Wilsonstheorem
6.7.Elementarypropertiesofquadraticresiduesandnon-residues
6.8.Theorderofa(modm)IslS
6.9.TheconverseofFermatstheorem
6.10.Divisibilityof2P-1_1byp
6.11.Gaussslemmaandthequadraticcharacterof
6.12.Thelawofreciprocity
6.13.Proofofthelawofreciprocity
6.14.Testsfororimalitv
6.15.FactorsofMersennenumbers;atheoremofEuler

Ⅶ.GENERALPROPERTIESOFCONGRUENCES
7.1.Rootsofcongruences
7.2.Integralpolynomialsandidenticalcongruences
7.3.Divisibilityofpolynomials(modm)
7.4.Rootsofc~nmuencestoaorimemodulus
7.5.Someapplicationsofthegeneraltheorems
7.6.LagrangesproofofFermatsandWilsonstheorems
7.7.Theresidueof{1/2(p-1)}!
7.8.AtheoremofWolstenholme
7.9.ThetheoremofvonStaudt
7.10.ProofofvonStaudtstheorem

Ⅷ.CONGRUENCESTOCOMPOSITEMODULI
8.1.Linearcongruences
8.2.Congruencesofhigherdegree
8.3.Congruencestoaorime-oowermodulus
8.4.Examoles
8.5.Bauersidenticalcongruence
8.6.Bauerscongruence：thecasep=
8.7.AtheoremofLeudesdorf
8.8.FurtherconsequencesofBauerstheorem
8.9.Theresiduesof2P-1and(p-1)!tomodulusp

Ⅸ.THEREPRESENTATIONOFNUMBERSBYDECIMALS
9.1.Thedecimalassociatedwithagivennumber
9.2.Terminatingandrecurringdecimals
9.3.Representationofnumbersinotherscales
9.4.Irrationalsdefinedbydecimals
9.5.Testsfordivisibility
9.6.Decimalswiththemaximumperiod
9.7.Bachetsproblemoftheweights
9.8.ThegameofNim
9.9.Integerswithmissingdigits
9.10.Setsofmeasurezero
9.11.Decimalswithmissingdigits
9.12.Normalnumbers
9.13.Proofthatalmostallnumbersarenormal

Ⅹ.CONTINUEDFRACTIONS
10.1.Finitecontinuedfractions
10.2.Convementstoacontinuedfraction
10.3.Continuedfractionswithpositivequotients
10.4.Simplecontinuedfractions
10.5.Therepresentationofanirreduciblerationalfractionbyasimplecontinuedfraction
10.6.ThecontinuedfractionalgorithmandEuclidsalgorithm
10.7.Thedifferencebetweenthefractionanditsconvergents
10.8.Infinitesimplecontinuedfractions
10.9.Therepresentationofanirrationalnumberbyaninfinitecontinuedfraction
10.10.Alemma
10.11.Equivalentnumbers
10.12.Periodiccontinuedfractions
10.13.SomesoecialQuadraticsurds
10.14.TheseriesofFibonacciandLucas
10.15.Approximationbyconvergents

Ⅺ.APPROXIMATIONOFIRRATIONALSBYRATIONALS
11.1.Statementoftheoroblem
11.2.Generalitiesconcerningtheproblem
11.3.AnargumentofDirichlet
11.4.Ordersofaporoximation
11.5.Aloohrnienncltranscendentalnumbers
11.6.Theexistenceoftranscendentalnumbers..
11.7.Liouvillestheoremandtheconstructionoftranscendentalnumbers
11.8.Themeasureoftheclosestapproximationstoanarbitraryirrational
11.9.Anothertheoremconcerningtheconvergentstoacontinuedfraction
11.10.Continuedfractionswithboundedquotients
11.11.Furthertheoremsconcerningapproximation
11.12.Simultaneousapproximation
11.13.Thetranscendenceofe
11.14.Thetranscendenceofπ

Ⅻ.THEFUNDAMENIALTHEOREMOFARITHMETICINk(1)，k(i)，ANDk(O)
12.1.Algebraicnumbersandintegers
12.2.Therationalintegers，theGaussianintegers，andtheintegersofk(p)
12.3.Euclidsalgorithm
12.4.AoolicationofEuclidsalgorithmtothefundamentaltheoremink(1)
12.5.HistoricalremarksonEuclidsalgorithmandthefundamentaltheorem
12.6.ProoertiesoftheGaussianintegers
12.7.Primesink(i)
12.8.Thefundnmentaltheoremofarithmeticink(i)
12.9.Theintegersofk(p)

ⅩⅢ.SOMEDIOPHANTINEEQUATIONS
13.1.Fermatslasttheorem
13.2.Theeauationxz4-vz=zz
13.3.Theequationx4-t-y4=z
13.4.Theequationx3+y3=z
13.5.Theequationx3+y3=3z
13.6.Theexoressionofarationalasasumofrationalcubes
13.7.Theequationx3+y3+z3=t

ⅩⅣ.OUADRATICFIELDS(1)
14.1.Algebraicfields
14.2.Algebraicnumbersandintegers：orimitivepolynomials
14.3.Thegeneralquadraticfieldk(√m)
14.4.Unitiesandorimes
14.5.Theunitiesofk(√2)
14.6.Fieldsinwhichthefundamentaltheoremisfalse
14.7.ComnlexEuclideanfields
14.8.RealEuclideanfields
14.9.RealEuclideanfields(continued)

ⅩⅤ.OUADRATICFIELDS(2)
15.1.Theorimesofk(i)
15.2.Fermatstheoremink(i)
15.3.Theprimesofk(p)
15.4.Theprimesofk(√2)andk(√5)
15.5.LucasstestfortheprimalityoftheMersennenumberM4n+
15.6.Generalremarksonthearithmeticofquadraticfields
15.7.Idealsinaquadraticfield
15.8.Otherfields

ⅩⅥ.THEARITHMETICALFUNCTIONSФ(n)，μ(n)，d(n)，σ(n)，r(n)
16.1.ThefunctionФ(n)
16.2.AfurtherproofofTheorem
16.3.TheMrbiusfunction
16.4.TheMrbiusinversionformula
16.5.Furtherinversionformulae
16.6.EvaluationofRamanuianssum
16.7.Thefunctionsd(n)andcrk(n)
16.8.Perfectnumbers
16.9.Thefunctionr(n)
16.10.Proofoftheformulaforr(n)

ⅩⅦ.GENERATINGFUNCTIONSOFARITHMETICALFUNCTIONS
17.1.ThegenerationofarithmeticalfunctionsbymeansofDirichletseries
17.2.Thezetafunction
17.3.Thebehaviourofξ(s)whens→
17.4.MultiplicationofDirichletseries
17.5.Thegeneratingfunctionsofsomespecialarithmeticalfunctions32~
17.6.TheanalyticalinterpretationoftheM6biusformula
17.7.ThefunctionA(n)
17.8.Furtherexamplesofgeneratingfunctions
17.9.Thegeneratingfunctionofr(n)
17.10.Generatingfunctionsofothertypes

ⅩⅧ.THEORDEROFMAGNITUDEOFARITHMETICALFUNCTIONS
18.1.Theorderofd(n)
18.2.Theaverageorderofd(n)
18.3.Theorderofσ(n)
18.4.TheorderofФ(n)
18.5.TheaverageorderofФ(n)
18.6.Thenumberofsquarefreenumbers
18.7.Theorderofσ(n)

ⅩⅨ.PARTITIONS
19.1.Thegeneralproblemofadditivearithmetic
19.2.Partitionsofnumbers
19.3.Thegeneratingfunctionofp(n)
19.4.Othergeneratingfunctions
19.5.TwotheoremsofEuler
19.6.Furtheralgebraicalidentities
19.7.AnotherformulaforF(x)
19.8.AtheoremofJacobi
19.9.SpecialcasesofJacobisidentity
19.10.ApplicationsofTheorem
19.11.ElementaryproofofTheorem
19.12.Congruencepropertiesofp(n)
19.13.TheRogers-Ramanujanidentities
19.14.ProofofTheorems362and
19.15.Ramanujanscontinuedfraction

ⅩⅩ.THEREPRESENTATIONOFANUMBERBYTWOORFOURSQUARES
20.1.Waringsproblem：thenumbersg(k)andG(k)
20.2.Squares
20.3.SecondproofofTheorem
20，4.ThirdandfourthproofsofTheorem
20.5.Thefour-squaretheorem
20.6.Quaternions
20.7.Preliminarytheoremsaboutintegralquatemions
20.8.Thehighestcommonfight-handdivisoroftwoquatemions
20.9.PrimequatemionsandtheproofofTheorem
20.10.Thevaluesofg(2)andG(2)
20.11.LemmasforthethirdproofofTheorem
20.12.ThirdproofofTheorem369：thenumberofrepresentations
20.13.Representationsbyalargernumberofsquares

ⅩⅩⅠ.REPRESENTATIONBYCUBESANDHIGHERPOWERS
21.1.Biquadrates
21.2.Cubes：theexistenceofG(3)andg(3)
21.3.Aboundforg(3)
21.4.Higherpowers
21.5.Alowerboundforg(k)
21.6.LowerboundsforG(k)
21.7.Sumsaffectedwithsigns：thenumberv(k)
21.8.Upperboundsforv(k)
21.9.TheproblemofProuhetandTarry：thenumberP(k，j)
21.10.EvaluationofP(k，j)forparticularkandj
21.11.FurtherproblemsofDiophantineanalysis

ⅩⅩⅡ.THESERIESOFPRIMES(3)
22.1.Thefunctions0(x)and$(x)
22.2.Proofthat0(x)and~(x)areoforderx
22.3.Bertrandspostulateandaformulaforprimes
22.4.ProofofTheorems7and
22.5.Twoformaltransformations
22.6.Animportantsum
22.7.Thesum12p~1andtheproductFI(1-p-1)
22.8.Mertensstheorem
22.9.ProofofTheorems323and
22.10.Thenumberofprimefactorsofn
22.11.Thenormalorderofto(n)andf2(n)
22.12.Anoteonroundnumbers
22.13.Thenormalorderofd(n)
22.14.Selbergstheorem
22.15.ThefunctionsR(x)andV(ξ)
22.16.CompletionoftheproofofTheorems434，6，and
22.17.ProofofTheorem
22.18.Productsofkprimefactors
22.19.Primesinaninterval
22.20.Aconjectureaboutthedistributionofprimepairsp，p+

ⅩⅩⅢ.KRONECKERSTHEOREM
23.1.Kroneckerstheoreminonedimension
23.2.Proofsoftheone-dimensionaltheorem
23.3.Theproblemofthereflectedray
23.4.Statementofthegeneraltheorem
23.5.Thetwoformsofthetheorem
23.6.Anillustration
23.7.Lettenmeyersproofofthetheorem
23.8.Estermannsproofofthetheorem
23.9.Bohrsproofofthetheorem
23.10.Uniformdistribution

ⅩⅩⅣ.GEOMETRYOFNUMBERS
24.1.Introductionandrestatementofthefundamentaltheorem
24.2.Simpleapplications
24.3.ArithmeticalproofofTheorem
24.4.Bestpossibleinequalities
24.5.Thebestpossibleinequalityforξ2+n
24.6.Thebestpossibleinequalityfor|ξn|
24.7.Atheoremconcerningnon-homogeneousforms
24.8.ArithmeticalproofofTheorem
24.9.Tchebotarefstheorem
24.10.AconverseofMinkowskisTheorem

ⅩⅩⅤ.ELLIPTICCURVES
25.1.Thecongruentnumberproblem
25.2.Theadditionlawonanellipticcurve
25.3.Otherequationsthatdefineellipticcurves
25.4.Pointsoffiniteorder
25.5.Thegroupofrationalpoints
25.6.Thegroupofpointsmodulop.
25.7.Integerpointsonellipticcurves
25.8.TheL-seriesofanellipticcurve
25.9.Pointsoffiniteorderandmodularcurves
25.10.EllipticcurvesandFermatslasttheorem

APPENDIX
1.Anotherformulaforpn
2.AgeneralizationofTheorem
3.Unsolvedproblemsconcerningprimes
ALISTOFBOOKS
INDEXOFSPECIALSYMBOLSANDWORDS
INDEXOFNAMES
GENERALINDEX