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Book Cover
Author Artin, Emil, 1898-1962, author

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 Correspondence1
2.Emil Artin, his life and his work18
3.Reminiscing Helmut Hasse25
4.Reciprocity Laws for Power Residues33
5.Class Field Theory38
6.Time Table41
pt. II The Letters45
1.1923--192647, Letter from Artin to Hasse48, Postcard from Artin to Hasse51
3.Date unknown, Letter from Artin to Hasse52
4.Date unknown, Letter from Artin to Hasse56, Postcard from Artin to Hasse59
 Comments on Letters 1-5 
5.1.The Prehistory62
5.2.Hasse's Lecture in Hamburg63
5.3.Artin's Inversion Method64
5.4.Second Supplementary Law68
5.5.General Reciprocity Law72
5.6.The Article on X-Series73
5.7.The Gap 1923--192677, Letter from Artin to Hasse81
6.1.Complex Multiplication88
6.3.Eisenstein's reciprocity law92
6.4.Cubic Gauss Sums93
6.5.Chebotarev's Article96, Letter from Artin to Hasse101
7.1.Eisenstein's Method103
2.1927105, Letter from Artin to Hasse107
8.1.Artin's Course in 1927109
8.2.The Jacobi Symbol110
8.3.Hasse's Plans for the Annalen113, Letter from Artin to Hasse117
9.1.The Proof125
9.2.The Method of Abelian Crossing125
9.3.The Lemma129
9.4.Furtwangler's Trick130, Letter from Artin to Hasse135
10.1.The σ-Formulation138
10.2.Extension of the Jacobi Symbol139
10.3.The Hilbert Symbol143
10.4.The Inversion Factor146
10.5.Part II of Hasse's Report on Class Field Theory147, Letter from Artin to Hasse149
11.1.Primary and Hyperprimary Numbers152
11.2.On the Biquadratic Reciprocity Law152
11.3.Class Number Divisibility154, Letter from Artin to Hasse158
12.1.The Structure of Class Field Theory160, Letter from Artin to Hasse164
13.1.On the Principal Ideal Theorem169, Letter from Artin to Hasse175
14.1.Relative Units178
14.2.Artin-Schreier and the Beautiful Formula179, Letter from Artin to Hasse184
15.1.On the Class Field Tower188
15.2.Class Field Theory for Function Fields194
15.3.The Concept for Part II of Hasse's Report196
15.4.Non-abelian Extensions199, Letter from Artin to Hasse201
16.1.The Second Supplementary Law204, Letter from Artin to Hasse205
17.2.Joint Article on the Supplementary Laws211
17.3.Artin's Conjecture on Primitive Roots213
17.4.Explicit Formulas for the Reciprocity Law216
17.5.Minkowski and the Unit Theorem217
3.1928--1929219, Letter from Artin to Hasse221
18.1.The Theorem of Jordan-Holder-Schreier223
18.2.The Hamburg Meeting 1928223
18.3.Hasse's Diary Entry224, Letter from Artin to Hasse226
19.1.On the Density Theorem228, Letter from Artin to Hasse229
20.1.Arnold Scholz231, Letter from Artin to Hasse235
21.1.Furtwangler's Conjecture236, Letter from Artin to Hasse239
22.1.Complex Quadratic Base Fields241
22.2.Ambiguous ideal classes241
22.3.Hasse's Generalization242
22.4.The group theoretic approach242
22.5.On Part II of Hasse's Report on Class Field Theory243, Letter from Artin to Hasse245, Letter from Artin to Hasse247, Letter from Artin to Hasse249
25.1.Quadratic Forms250
25.2.Metabelian Groups251, Letter from Artin to Hasse252
26.1.Hasse's Norm Residue Symbol253
26.2.Local Class Field theory254
26.3.Further Developments255
26.4.Ideal Theory256, Letter from Artin to Hasse259
27.1.Petersson260, Letter from Artin to Hasse262
28.2.Continuous Groups263
4.1930--1934265, Letter from Artin to Hasse268
29.1.The Proof Sheets270
29.2.Norm Residues270
29.3.The Inversion Factor271, Letter from Artin to Hasse273
30.3.Weddle286, Letter from Artin to Hasse288
31.1.Two Publications293
31.2.Hasse's Article on the Conductor294
31.3.Book Projects295
31.4.Olga Taussky296, Letter from Artin to Hasse299
32.1.Hasse's Communication303
32.2.The detour304, Letter from Artin to Hasse306
33.1.The Conductor Manuscript307
33.3.Future Prospects308
33.4.Without Class Field Theory309, Letter from Artin to Hasse313
34.1.The Remarks315
34.2.Zukunftsmusik316, Letter from Artin to Hasse318
35.2.Hypercomplex Arithmetic321
35.3.Publication of Hasse's Report323, Letter from Artin to Hasse325
36.1.Conjectures on Algebras327
36.2.The Gamma Function328
36.3.Schreier-Sperner328, Letter from Artin to Hasse330
37.1.Icosahedral Extension332, Letter from Artin to Hasse334
38.1.Maximal Orders339
38.3.Tremendous Simplifications343, Letter from Artin to Hasse349
39.1.The Hensel Volume350
39.2.The Class Field Theory Proofs351
39.4.The Theorem on Skew Fields354
40.November 1931, Letter from Artin to Hasse356
40.1.Cyclicity of Simple Algebras358
40.2.Artin's Amateurish Steps359
41.1932, Letter from Artin to Hasse362
41.1.Continuation of L-Series364
41.2.Algebras365, Letter from Artin to Hasse369
42.1.First Letter on Factor Systems374, Letter from Artin to Hasse378, Postcard from Artin to Hasse380 16.03.1932, Letter from Artin to Hasse381, Letter from Artin to Hasse387
46.1.Last Letter on Factor Systems390, Letter from Hasse to Artin392
47.1.Artin's Class Field Theory Lectures396
47.2.The Inverse Theorem397, Letter from Artin to Hasse402
48.1.The Proof of the Principal Ideal Theorem404
48.2.Hasse's Visit in Hamburg405, Letter from Artin to Hasse406
49.1.Hasse's Work on the Riemann Conjecture in Function 
50.1934, Letter from Artin to Hasse409
5.1937--1938411, Letter from Hasse to Artin412
51.1.Hasse's Visit413
51.2.Alice in Wonderland414
52.Nov. 1938, Natascha Artin to Hasse, undated [Bloomington]415, Letter from Hasse to Artin417
53.1.Hecke's Visit419
53.2.The Class Field Tower419
53.3.The Blue Hasse420
6.1953--1958423, Letter from Artin to Hasse425
54.1.Artin's algebra seminar 1953/54427
54.2.Artin-Tate427, Letter from Hasse to Artin429
55.1.Scholz's Number Knots431
55.2.Artin Root Numbers431, Postcard from Artin to Hasse [Tokyo]433
56.1.Tokyo-Nikko 1955434
56.2.Studium Generale435, Postcard from Hasse to Artin436, Letter from Artin to Hasse437, Letter from Hasse to Artin438
59.1.Ernst Witt439, Letter from Hasse to Artin440, Letter from Artin to Hasse [Gottingen]441, Letter from Hasse to Artin442, Letter from Artin to Hasse [Princeton]443, Letter from Hasse to Artin444, Letter from Hasse to Artin445, Letter from Artin to Hasse [Princeton]446, Letter from Artin to Hasse [Princeton]447, Letter from Artin to Hasse [Princeton]448, Letter from Hasse to Artin [Ahrensburg]449, Letter from Artin to Hasse [Princeton]451, Letter from Hasse to Artin452, Letter from Artin to Hasse [Princeton]453, Letter from Hasse to Artin454
74.Report on Artin455
 Author Index477
 Subject Index481
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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
Subject Artin, Emil, 1898-1962 -- Correspondence.
Hasse, Helmut, 1898-1979 -- Correspondence.
Mathematicians -- Austria -- Correspondence.
Mathematicians -- Germany -- Correspondence.
Genre/Form Collected Correspondence.
Records and correspondence.
Personal correspondence.
Form Electronic book
Author Frei, Günther, editor
Hasse, Helmut, 1898-1979, author
Lemmermeyer, Franz, 1962- editor, translator
Roquette, Peter, 1927- editor
ISBN 3034807147
3034807155 (electronic bk.)
9783034807159 (electronic bk.)