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国外很好数学著作原版系列拉马努金遗失笔记(第3卷) 内容简介
拉马努金数学遗失笔记,包括了S. Ramanujan在1988年由Narosa出版的《Lost Notebook and Other Unpublished Papers》和其他未发表的论文中提出的所有主张。这本书包含了“遗失的笔记”，它是1976年春天由作者在剑桥三一学院图书馆发现的。其中还包含其他部分手稿、碎片和拉马努金1917年-1919年在疗养院写给G.H.哈迪的信件。这是五卷中的第三卷包含10章，集中在一些丢失的笔记和其他未发表的论文中很重要和很有影响的材料。中间是配分函数，有三章专门讨论了等级和分区的曲柄。此外，还对拉马努金手写稿上的划分和tau函数进行了研究。
国外很好数学著作原版系列拉马努金遗失笔记(第3卷) 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5 Ramanujan,s Unpublished Manuscript on the Partition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)................1295. 19 Divisibility of T(n)for Almost All Values of n 5.20 The Congruence p(5n 4)=0(mod 5), Revisited......1325.21 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 235.18 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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