close
1.

電子ブック
ＥＢ
1. The Mathematical Legacy of Srinivasa Ramanujan
by M. Ram Murty, V. Kumar Murty
出版情報: India : Springer India : Imprint: Springer, 2013
オンライン: http://dx.doi.org/10.1007/978-81-322-0770-2
所蔵情報: loading…
目次情報: 続きを見る
Preface
Chapter 1. The Legacy of Srinivasa Ramanujan
Chapter 2. The Ramanujan tau function
Chapter 3. Ramanujan’s conjecture and l-adic representations
Chapter 4. The Ramanujan conjecture from GL(2) to GL(n)
Chapter 5. The circle method
Chapter 6. Ramanujan and transcendence
Chapter 7. Arithmetic of the partition function
Chapter 8. Some nonlinear identities for divisor functions
Chapter 9. Mock theta functions and mock modular forms
Chapter 10. Prime numbers and highly composite numbers
Chapter 11. Probabilistic number theory
Chapter 12. The Sato-Tate conjecture for the Ramanujan tau-function
Bibliography
Index
Preface
Chapter 1. The Legacy of Srinivasa Ramanujan
Chapter 2. The Ramanujan tau function
2.

電子ブック
ＥＢ
2. Transcendental Numbers
by M. Ram Murty, Purusottam Rath
出版情報: New York, NY : Springer New York : Imprint: Springer, 2014
オンライン: http://dx.doi.org/10.1007/978-1-4939-0832-5
所蔵情報: loading…
目次情報: 続きを見る
1. Liouville’s theorem
2. Hermite’s Theorem
3. Lindemann’s theorem
4. The Lindemann-Weierstrass theorem
5. The maximum modulus principle
6. Siegel’s lemma
7. The six exponentials theorem
8. Estimates for derivatives
9. The Schneider-Lang theorem
10. Elliptic functions
11. Transcendental values of elliptic functions
12. Periods and quasiperiods
13. Transcendental values of some elliptic integrals
14. The modular invariant
15. Transcendental values of the j-function
16. More elliptic integrals
17. Transcendental values of Eisenstein series
18. Elliptic integrals and hypergeometric series
19. Baker’s theorem
20. Some applications of Baker’s theorem
21. Schanuel’s conjecture
22. Transcendental values of some Dirichlet series
23. Proof of the Baker-Birch-Wirsing theorem
24. Transcendence of some infinite series
25. Linear independence of values of Dirichlet L-functions
26. Transcendence of values of modular forms
27. Transcendence of values of class group L-functions
28. Periods, multiple zeta functions and (3).
1. Liouville’s theorem
2. Hermite’s Theorem
3. Lindemann’s theorem
3.

電子ブック
ＥＢ
3. Problems in Analytic Number Theory. 2
by M. Ram Murty
出版情報: New York, NY : Springer Science+Business Media, LLC, 2008
シリーズ名: Graduate Texts in Mathematics ; 206
オンライン: http://dx.doi.org/10.1007/978-0-387-72350-1
所蔵情報: loading…
4.

電子ブック
ＥＢ
4. A First Course in Graph Theory and Combinatorics : Second Edition. 2nd ed. 2022
by Sebastian M. Cioabă, M. Ram Murty
出版情報: Singapore : Springer Nature Singapore : Imprint: Springer, 2022
シリーズ名: Texts and Readings in Mathematics ; 55
オンライン: https://doi.org/10.1007/978-981-19-0957-3
所蔵情報: loading…
目次情報: 続きを見る
Chapter 1. Basic Graph Theory
Chapter 2. Basic Counting
Chapter 3. The Principle of Inclusion and Exclusion
Chapter 4. Graphs and Matrices
Chapter 5. Trees
Chapter 6. M¨obius Inversion and Graph Colouring
Chapter 7. Enumeration under Group Action
Chapter 8. Matching Theory
Chapter 9. Block Designs
Chapter 10. Planar Graphs
Chapter 11. Edges and Cycles
Chapter 12. Expanders and Ramanujan Graphs
Chapter 13. Hints
Chapter 1. Basic Graph Theory
Chapter 2. Basic Counting
Chapter 3. The Principle of Inclusion and Exclusion
5.

電子ブック
ＥＢ
5. A Second Course in Analysis. 1st ed. 2022
by M. Ram Murty
出版情報: Singapore : Springer Nature Singapore : Imprint: Springer, 2022
シリーズ名: IMSc Lecture Notes in Mathematics ;
オンライン: https://doi.org/10.1007/978-981-16-7246-0
所蔵情報: loading…
目次情報: 続きを見る
1. Background
2. Measure Theory
3. Fourier Transforms
4. Complex Analysis
5. Introduction to Algebraic Topology
Index
1. Background
2. Measure Theory
3. Fourier Transforms