《拉馬努金遺失筆記（第三卷）》是2019年6月哈爾濱工業大學出版社出版的書籍，作者是(美)喬治·E.安德魯斯，本書主要講了印度神奇數學家拉馬努金有著深邃的數學直覺和洞察力，這套叢書給出了拉馬努金很多漂亮的數學結果，共分為4卷。本書為第3卷，主要介紹了函式值、模函式與Q函式的特性、無窮級數等內容。
基本介紹
- 中文名：拉馬努金遺失筆記（第三卷）
- 作者：(美)喬治·E.安德魯斯
- 出版社：哈爾濱工業大學出版社
- ISBN：9787560381381
圖書目錄
- 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
4.54CongruencesFurtherEntriesfor theon PagesCoefficients58andAn59 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5 Ramanujan,s Unpublished Manuscript on the Partition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
附錄I拉馬努金的中國知音:數學家劉治國的“西天取經”之旅附錄II劉治國教授訪談
編輯手記
