Table of Contents |
pt. I | Introduction to the Correspondence | 1 |
1. | Introduction | 3 |
2. | Emil Artin, his life and his work | 18 |
3. | Reminiscing Helmut Hasse | 25 |
4. | Reciprocity Laws for Power Residues | 33 |
5. | Class Field Theory | 38 |
6. | Time Table | 41 |
pt. II | The Letters | 45 |
1. | 1923--1926 | 47 |
1. | 09.07.1923, Letter from Artin to Hasse | 48 |
2. | 09.07.1923, Postcard from Artin to Hasse | 51 |
3. | Date unknown, Letter from Artin to Hasse | 52 |
4. | Date unknown, Letter from Artin to Hasse | 56 |
5. | 12.07.1923, Postcard from Artin to Hasse | 59 |
| Comments on Letters 1-5 | |
5.1. | The Prehistory | 62 |
5.2. | Hasse's Lecture in Hamburg | 63 |
5.3. | Artin's Inversion Method | 64 |
5.4. | Second Supplementary Law | 68 |
5.5. | General Reciprocity Law | 72 |
5.6. | The Article on X-Series | 73 |
5.7. | The Gap 1923--1926 | 77 |
6. | 10.02.1926, Letter from Artin to Hasse | 81 |
| Comments | |
6.1. | Complex Multiplication | 88 |
6.2. | Topology | 91 |
6.3. | Eisenstein's reciprocity law | 92 |
6.4. | Cubic Gauss Sums | 93 |
6.5. | Chebotarev's Article | 96 |
7. | 10.09.1926, Letter from Artin to Hasse | 101 |
7.1. | Eisenstein's Method | 103 |
2. | 1927 | 105 |
8. | 17.07.1927, Letter from Artin to Hasse | 107 |
8.1. | Artin's Course in 1927 | 109 |
8.2. | The Jacobi Symbol | 110 |
8.3. | Hasse's Plans for the Annalen | 113 |
9. | 19.07.1927, Letter from Artin to Hasse | 117 |
9.1. | The Proof | 125 |
9.2. | The Method of Abelian Crossing | 125 |
9.3. | The Lemma | 129 |
9.4. | Furtwangler's Trick | 130 |
10. | 21.07.1927, Letter from Artin to Hasse | 135 |
10.1. | The σ-Formulation | 138 |
10.2. | Extension of the Jacobi Symbol | 139 |
10.3. | The Hilbert Symbol | 143 |
10.4. | The Inversion Factor | 146 |
10.5. | Part II of Hasse's Report on Class Field Theory | 147 |
11. | 26.07.1927, Letter from Artin to Hasse | 149 |
11.1. | Primary and Hyperprimary Numbers | 152 |
11.2. | On the Biquadratic Reciprocity Law | 152 |
11.3. | Class Number Divisibility | 154 |
12. | 29.07.1927, Letter from Artin to Hasse | 158 |
12.1. | The Structure of Class Field Theory | 160 |
13. | 02.08.1927, Letter from Artin to Hasse | 164 |
13.1. | On the Principal Ideal Theorem | 169 |
14. | 06.08.1927, Letter from Artin to Hasse | 175 |
14.1. | Relative Units | 178 |
14.2. | Artin-Schreier and the Beautiful Formula | 179 |
15. | 19.08.1927, Letter from Artin to Hasse | 184 |
15.1. | On the Class Field Tower | 188 |
15.2. | Class Field Theory for Function Fields | 194 |
15.3. | The Concept for Part II of Hasse's Report | 196 |
15.4. | Non-abelian Extensions | 199 |
16. | 04.09.1927, Letter from Artin to Hasse | 201 |
16.1. | The Second Supplementary Law | 204 |
17. | 27.10.1927, Letter from Artin to Hasse | 205 |
17.1. | Reichenberg | 211 |
17.2. | Joint Article on the Supplementary Laws | 211 |
17.3. | Artin's Conjecture on Primitive Roots | 213 |
17.4. | Explicit Formulas for the Reciprocity Law | 216 |
17.5. | Minkowski and the Unit Theorem | 217 |
3. | 1928--1929 | 219 |
18. | 05.08.1928, Letter from Artin to Hasse | 221 |
18.1. | The Theorem of Jordan-Holder-Schreier | 223 |
18.2. | The Hamburg Meeting 1928 | 223 |
18.3. | Hasse's Diary Entry | 224 |
19. | 04.11.1928, Letter from Artin to Hasse | 226 |
19.1. | On the Density Theorem | 228 |
20. | 14.11.1928, Letter from Artin to Hasse | 229 |
20.1. | Arnold Scholz | 231 |
21. | 18.11.1928, Letter from Artin to Hasse | 235 |
21.1. | Furtwangler's Conjecture | 236 |
22. | 19.11.1928, Letter from Artin to Hasse | 239 |
22.1. | Complex Quadratic Base Fields | 241 |
22.2. | Ambiguous ideal classes | 241 |
22.3. | Hasse's Generalization | 242 |
22.4. | The group theoretic approach | 242 |
22.5. | On Part II of Hasse's Report on Class Field Theory | 243 |
23. | 22.11.1928, Letter from Artin to Hasse | 245 |
24. | 03.12.1928, Letter from Artin to Hasse | 247 |
25. | 12.01.1929, Letter from Artin to Hasse | 249 |
25.1. | Quadratic Forms | 250 |
25.2. | Metabelian Groups | 251 |
26. | 10.05.1929, Letter from Artin to Hasse | 252 |
26.1. | Hasse's Norm Residue Symbol | 253 |
26.2. | Local Class Field theory | 254 |
26.3. | Further Developments | 255 |
26.4. | Ideal Theory | 256 |
27. | 19.05.1929, Letter from Artin to Hasse | 259 |
27.1. | Petersson | 260 |
28. | 15.12.1929, Letter from Artin to Hasse | 262 |
28.1. | Suetuna | 263 |
28.2. | Continuous Groups | 263 |
4. | 1930--1934 | 265 |
29. | 23.08.1930, Letter from Artin to Hasse | 268 |
29.1. | The Proof Sheets | 270 |
29.2. | Norm Residues | 270 |
29.3. | The Inversion Factor | 271 |
30. | 18.09.1930, Letter from Artin to Hasse | 273 |
30.1. | L-series | 279 |
30.2. | In-primary | 286 |
30.3. | Weddle | 286 |
31. | 23.09.1930, Letter from Artin to Hasse | 288 |
31.1. | Two Publications | 293 |
31.2. | Hasse's Article on the Conductor | 294 |
31.3. | Book Projects | 295 |
31.4. | Olga Taussky | 296 |
32. | 10.10.1930, Letter from Artin to Hasse | 299 |
32.1. | Hasse's Communication | 303 |
32.2. | The detour | 304 |
33. | 07.11.1930, Letter from Artin to Hasse | 306 |
33.1. | The Conductor Manuscript | 307 |
33.2. | Speiser | 307 |
33.3. | Future Prospects | 308 |
33.4. | Without Class Field Theory | 309 |
34. | 11.11.1930, Letter from Artin to Hasse | 313 |
34.1. | The Remarks | 315 |
34.2. | Zukunftsmusik | 316 |
35. | 27.11.1930, Letter from Artin to Hasse | 318 |
35.1. | Corrections | 320 |
35.2. | Hypercomplex Arithmetic | 321 |
35.3. | Publication of Hasse's Report | 323 |
36. | 24.01.1931, Letter from Artin to Hasse | 325 |
36.1. | Conjectures on Algebras | 327 |
36.2. | The Gamma Function | 328 |
36.3. | Schreier-Sperner | 328 |
37. | 06.05.1931, Letter from Artin to Hasse | 330 |
37.1. | Icosahedral Extension | 332 |
38. | 16.06.1931, Letter from Artin to Hasse | 334 |
38.1. | Maximal Orders | 339 |
38.2. | Siegel | 341 |
38.3. | Tremendous Simplifications | 343 |
39. | 24.08.1931, Letter from Artin to Hasse | 349 |
39.1. | The Hensel Volume | 350 |
39.2. | The Class Field Theory Proofs | 351 |
39.3. | Herbrand | 352 |
39.4. | The Theorem on Skew Fields | 354 |
40. | November 1931, Letter from Artin to Hasse | 356 |
40.1. | Cyclicity of Simple Algebras | 358 |
40.2. | Artin's Amateurish Steps | 359 |
41. | 1932, Letter from Artin to Hasse | 362 |
41.1. | Continuation of L-Series | 364 |
41.2. | Algebras | 365 |
42. | 09.03.1932, Letter from Artin to Hasse | 369 |
42.1. | First Letter on Factor Systems | 374 |
43. | 10.03.1932, Letter from Artin to Hasse | 378 |
44. | 11.03.1932, Postcard from Artin to Hasse | 380 |
45. | ca. 16.03.1932, Letter from Artin to Hasse | 381 |
46. | 02.05.1932, Letter from Artin to Hasse | 387 |
46.1. | Last Letter on Factor Systems | 390 |
47. | 08.11.1932, Letter from Hasse to Artin | 392 |
47.1. | Artin's Class Field Theory Lectures | 396 |
47.2. | The Inverse Theorem | 397 |
48. | 02.12.1932, Letter from Artin to Hasse | 402 |
48.1. | The Proof of the Principal Ideal Theorem | 404 |
48.2. | Hasse's Visit in Hamburg | 405 |
49. | 17.01.1934, Letter from Artin to Hasse | 406 |
49.1. | Hasse's Work on the Riemann Conjecture in Function | |
| Fields | 407 |
50. | 1934, Letter from Artin to Hasse | 409 |
5. | 1937--1938 | 411 |
51. | 14.01.1937, Letter from Hasse to Artin | 412 |
51.1. | Hasse's Visit | 413 |
51.2. | Alice in Wonderland | 414 |
52. | Nov. 1938, Natascha Artin to Hasse, undated [Bloomington] | 415 |
53. | 09.12.1938, Letter from Hasse to Artin | 417 |
53.1. | Hecke's Visit | 419 |
53.2. | The Class Field Tower | 419 |
53.3. | The Blue Hasse | 420 |
6. | 1953--1958 | 423 |
54. | 12.03.1953, Letter from Artin to Hasse | 425 |
54.1. | Artin's algebra seminar 1953/54 | 427 |
54.2. | Artin-Tate | 427 |
55. | 20.03.1953, Letter from Hasse to Artin | 429 |
55.1. | Scholz's Number Knots | 431 |
55.2. | Artin Root Numbers | 431 |
56. | 08.10.1955, Postcard from Artin to Hasse [Tokyo] | 433 |
56.1. | Tokyo-Nikko 1955 | 434 |
56.2. | Studium Generale | 435 |
57. | 20.10.1955, Postcard from Hasse to Artin | 436 |
58. | 20.02.1956, Letter from Artin to Hasse | 437 |
59. | 20.02.1956, Letter from Hasse to Artin | 438 |
59.1. | Ernst Witt | 439 |
60. | 18.12.1956, Letter from Hasse to Artin | 440 |
61. | 04.01.1957, Letter from Artin to Hasse [Gottingen] | 441 |
62. | 11.01.1957, Letter from Hasse to Artin | 442 |
63. | 15.11.1957, Letter from Artin to Hasse [Princeton] | 443 |
64. | 28.11.1957, Letter from Hasse to Artin | 444 |
65. | 13.12.1957, Letter from Hasse to Artin | 445 |
66. | 15.12.1957, Letter from Artin to Hasse [Princeton] | 446 |
67. | 20.01.1958, Letter from Artin to Hasse [Princeton] | 447 |
68. | 11.03.1958, Letter from Artin to Hasse [Princeton] | 448 |
69. | 20.03.1958, Letter from Hasse to Artin [Ahrensburg] | 449 |
70. | 02.04.1958, Letter from Artin to Hasse [Princeton] | 451 |
71. | 09.04.1958, Letter from Hasse to Artin | 452 |
72. | 17.04.1958, Letter from Artin to Hasse [Princeton] | 453 |
73. | 23.04.1958, Letter from Hasse to Artin | 454 |
74. | Report on Artin | 455 |
| References | 459 |
| Author Index | 477 |
| Subject Index | 481 |