Title Emil Artin and Helmut Hasse : the correspondence, 1923-1958 / Günther Frei, Franz Lemmermeyer, Peter J. Roquette, editors ; translated from the German by Franz Lemmermeyer

Published Basel : Springer, 2014

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

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Description 1 online resource (xx, 484 pages) : illustrations Series Contributions in Mathematical and Computational Sciences, 2191-303X ; volume 5 Contributions in mathematical and computational sciences ; v. 5. 2191-303X Contents Part I: Introduction to the Correspondence -- 1. Introduction -- 2. Emil Artin, his Life and his Work -- 3. Reminiscing Helmut Hasse -- 4. Reciprocity Laws for Power Residues -- 5. Class Field Theory -- 6. Time Table -- Part II: The Letters Summary This volume presents English translations of the letters exchanged between Emil Artin and Helmut Hasse written from 1921 to 1958. The letters are accompanied by extensive comments explaining the mathematical background and providing other essential context. Most letters deal with class field theory and shed new light on the birth of one of its most profound results: Artin's reciprocity law Notes "Originally published under the title "Emil Artin und Helmut Hasse: die Korrespondenz 1923-1934." Bibliography Includes bibliographical references and indexes Notes English Online resource; title from PDF title page (SpringerLink, viewed January 20, 2014) In Springer eBooks Subject Artin, Emil, 1898-1962 -- Correspondence Hasse, Helmut, 1898-1979 -- Correspondence SUBJECT Artin, Emil, 1898-1962 fast Hasse, Helmut, 1898-1979 fast Subject Mathematicians -- Austria -- Correspondence Mathematicians -- Germany -- Correspondence Mathematics. Mathematics MATHEMATICS -- Essays. MATHEMATICS -- Pre-Calculus. MATHEMATICS -- Reference. Mathematics Mathematicians Austria Germany Genre/Form personal correspondence. Personal correspondence Personal correspondence. Correspondance privée. Form Electronic book Author Frei, Günther, editor. Hasse, Helmut, 1898-1979, author. Lemmermeyer, Franz, 1962- editor, translator. Roquette, Peter, 1927- editor. ISBN 9783034807159 3034807155 3034807147 9783034807142

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