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拉马努金遗失笔记（第三卷）
作者：（美）乔治.E.安德鲁斯,（美）布鲁斯.C.伯恩特
出版社：哈尔滨工业大学出版社
出版时间：2019-06-01
ISBN：9787560381381
定价：¥109.00
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内容简介
暂缺《拉马努金遗失笔记（第三卷）》简介
作者简介
暂缺《拉马努金遗失笔记（第三卷）》作者简介
目录
Introduction
Ranks and Cranks, Part I
2.1 Introduction 9
2.2 Proof of Entry 2.1.1
2.3 Background for Entries 2.1.2 and 2.1.4
2.4 Proof of Entry 2.1.2
2.5 Proof of Entry 2.1.4
2.6 Proof of Entry 2.1.5
3 Ranks and Cranks, Part II
3.1 Introduction
32 Preliminary Results.……………
3.3 The 2-Dissection for F(a) .............
3.4 The 3-Dissection for F(q
3.5 The 5-Dissection for F(q)
3.6 The 7-Dissection for F(a
3.7 The 1l-Dissection for F(a
3.8 Conclusion
4 Ranks and Cranks. Part III
4.1 Introduction
4.2 Key Formulas on Page 59..'o3
4.3 Proofs of Entries 4.2.1 and 4.2.3
4.54 CongruencesFurtherEntriesfor theon PagesCoefficients58and An59 on Pages 179 and 180 74
4.6 Page 181: Partitions and Factorizations of Crank Coefficients. 82
4.7 Series on Pages 63 and 64 Related to Cranks
4.8 Ranks and Cranks: Ramanujan's Influence Continues..,..86
4.8.1 Congruences and Related Work
4.8.2 Asymptotics and Related Analysis
4.8.3 Combinatorics
4.8.4 Inequalities
4.8.5 Generalizations
5 Ramanujan,s Unpublished Manuscript on the Partition
and Tau Functions
5.0 Congruences for T(n)
5.1 The Congruence p(5n 4)=0(mod 5)
5.2 Divisibility of r(n) by 5
53 The Congruence p(257 24)≡0(mod25)………97
5.4 Congruences Modulo 5k
5.5 Congruences Modulo 7
5.6 Congruences Modulo 7, Continued
5.7 Congruences Modulo 49
58 Congruences Modulo49, Continued..………104
5.9 The Congruence p(1ln 6)=0(mod 11)
5.10 Congruences Modulo11, Continued..……………107
11 Divisibility by 2 or 3
5.12 Divisibility of T(n)
13 Congruences Modulo 13..................................119
5.14 Congruences for p(n) Modulo 13
5.15 Congruences to Further Prime Moduli........... 123 5.16 Congruences for p(n) Modulo 17, 19, 23, 29, or 31.......... 125 57 Divisibility of T(n)by23...……127 5. 18 The Congruence p(121n-5)=0(mod 121)................ 129 5. 19 Divisibility of T(n)for Almost All Values of n 5.20 The Congruence p(5n 4)=0(mod 5), Revisited...... 132 5.21 The Congruence p(25n 24)=0(mod 25), Revisited......... 134
5.22 Congruences for p(n) Modulo Higher Powers of 5
5.23 Congruences for p(n) Modulo Higher Powers of 5, Continued. 136
5.24 The Congruence p(7n 5)=0(mod 7)
5.25 Commentary..,.… 1 The Congruence p(5n 4)=0(mod 5)
5.2 Divisibility of T (n) by 5
5.4 Congruences Modulo 5
5.5 Congruences Modulo 7............
56 Congruences Modulo7, Continued..……144
5.7 Congruences Modulo 49
58 Congruences Modulo49, Continued..……145
5.9 The Congruence p(117 6)≡0(mod11).………145
5.10 Congruences Modulo 11, Continued............ 146 11 Divisibility by 2 or 3 12 Divisibility of T(n)
5.13 Congruences Modulo 13
5.14 Congruences for p(n) Modulo 13
15 Congruences to Further Prime Moduli
5.16 Congruences for p(n) Modulo 17, 19, 23, 29, or 31 159
17 Divisibility of T(n) by 23 5.18 The Congruence p(12In-5)=0(mod 121)
5.19 Divisibility of T(n) for Almost All Values of n 177
5.20 The Congruence p(5n 4)=0(mod 5),Revisited 178
5.23 Congruences for p(n) Modulo Higher Powers of 5, Continued.179
5.24 The Congruence p(7n 5)=0(mod 7)
6 Theorems about the Partition Function on Pages 189 and
182 6.1 Introduction 6.2 The Identities for Modulus 5.............................. 183
6.3 The Identities for Modulus 7
6.4 Two Beautiful, False, but Correctable Claims of Ramanujan.193
6.5Page182.
6.6 Further Remarks
7 Congruences for Generalized Tau Functions on Page 178..205
7.1 Introduction
7.2 Proofs
8 Ramanujan's Forty Identities for the Rogers-Ramanujan
Functions
8.1 Introduction
8.2 Definitions and Preliminary Results
8.3 The Forty Identities
8.4 The Principal Ideas Behind the Proofs 229
8.5 Proofs of the 40 Entries 243
8.6 Other Identities for G(a) and H(g and Final Remarks...333
9 Circular Summation
1 Introduction............
9.2 Proof of Entry 9.1.1
9.3 Reformulations
9.4 Special Cases
10 Highly Composite Numbers
Scratch Work
Location Guide
Provenance
References
附录I拉马努金的中国知音:数学家刘治国的“西天取经”之旅附录II刘治国教授访谈
编辑手记
2.1 Introduction 9
2.2 Proof of Entry 2.1.1
2.3 Background for Entries 2.1.2 and 2.1.4
2.4 Proof of Entry 2.1.2
2.5 Proof of Entry 2.1.4
2.6 Proof of Entry 2.1.5
3 Ranks and Cranks, Part II
3.1 Introduction
32 Preliminary Results.……………
3.3 The 2-Dissection for F(a) .............
3.4 The 3-Dissection for F(q
3.5 The 5-Dissection for F(q)
3.6 The 7-Dissection for F(a
3.7 The 1l-Dissection for F(a
3.8 Conclusion
4 Ranks and Cranks. Part III
4.1 Introduction
4.2 Key Formulas on Page 59..'o3
4.3 Proofs of Entries 4.2.1 and 4.2.3
4.54 CongruencesFurtherEntriesfor theon PagesCoefficients58and An59 on Pages 179 and 180 74
4.6 Page 181: Partitions and Factorizations of Crank Coefficients. 82
4.7 Series on Pages 63 and 64 Related to Cranks
4.8 Ranks and Cranks: Ramanujan's Influence Continues..,..86
4.8.1 Congruences and Related Work
4.8.2 Asymptotics and Related Analysis
4.8.3 Combinatorics
4.8.4 Inequalities
4.8.5 Generalizations
5 Ramanujan,s Unpublished Manuscript on the Partition
and Tau Functions
5.0 Congruences for T(n)
5.1 The Congruence p(5n 4)=0(mod 5)
5.2 Divisibility of r(n) by 5
53 The Congruence p(257 24)≡0(mod25)………97
5.4 Congruences Modulo 5k
5.5 Congruences Modulo 7
5.6 Congruences Modulo 7, Continued
5.7 Congruences Modulo 49
58 Congruences Modulo49, Continued..………104
5.9 The Congruence p(1ln 6)=0(mod 11)
5.10 Congruences Modulo11, Continued..……………107
11 Divisibility by 2 or 3
5.12 Divisibility of T(n)
13 Congruences Modulo 13..................................119
5.14 Congruences for p(n) Modulo 13
5.15 Congruences to Further Prime Moduli........... 123 5.16 Congruences for p(n) Modulo 17, 19, 23, 29, or 31.......... 125 57 Divisibility of T(n)by23...……127 5. 18 The Congruence p(121n-5)=0(mod 121)................ 129 5. 19 Divisibility of T(n)for Almost All Values of n 5.20 The Congruence p(5n 4)=0(mod 5), Revisited...... 132 5.21 The Congruence p(25n 24)=0(mod 25), Revisited......... 134
5.22 Congruences for p(n) Modulo Higher Powers of 5
5.23 Congruences for p(n) Modulo Higher Powers of 5, Continued. 136
5.24 The Congruence p(7n 5)=0(mod 7)
5.25 Commentary..,.… 1 The Congruence p(5n 4)=0(mod 5)
5.2 Divisibility of T (n) by 5
5.4 Congruences Modulo 5
5.5 Congruences Modulo 7............
56 Congruences Modulo7, Continued..……144
5.7 Congruences Modulo 49
58 Congruences Modulo49, Continued..……145
5.9 The Congruence p(117 6)≡0(mod11).………145
5.10 Congruences Modulo 11, Continued............ 146 11 Divisibility by 2 or 3 12 Divisibility of T(n)
5.13 Congruences Modulo 13
5.14 Congruences for p(n) Modulo 13
15 Congruences to Further Prime Moduli
5.16 Congruences for p(n) Modulo 17, 19, 23, 29, or 31 159
17 Divisibility of T(n) by 23 5.18 The Congruence p(12In-5)=0(mod 121)
5.19 Divisibility of T(n) for Almost All Values of n 177
5.20 The Congruence p(5n 4)=0(mod 5),Revisited 178
5.23 Congruences for p(n) Modulo Higher Powers of 5, Continued.179
5.24 The Congruence p(7n 5)=0(mod 7)
6 Theorems about the Partition Function on Pages 189 and
182 6.1 Introduction 6.2 The Identities for Modulus 5.............................. 183
6.3 The Identities for Modulus 7
6.4 Two Beautiful, False, but Correctable Claims of Ramanujan.193
6.5Page182.
6.6 Further Remarks
7 Congruences for Generalized Tau Functions on Page 178..205
7.1 Introduction
7.2 Proofs
8 Ramanujan's Forty Identities for the Rogers-Ramanujan
Functions
8.1 Introduction
8.2 Definitions and Preliminary Results
8.3 The Forty Identities
8.4 The Principal Ideas Behind the Proofs 229
8.5 Proofs of the 40 Entries 243
8.6 Other Identities for G(a) and H(g and Final Remarks...333
9 Circular Summation
1 Introduction............
9.2 Proof of Entry 9.1.1
9.3 Reformulations
9.4 Special Cases
10 Highly Composite Numbers
Scratch Work
Location Guide
Provenance
References
附录I拉马努金的中国知音:数学家刘治国的“西天取经”之旅附录II刘治国教授访谈
编辑手记
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