Emil Artin and Helmut Hasse : The Correspondence 1923-1958

By: Frei, GüntherContributor(s): Lemmermeyer, Franz | Roquette, Peter JMaterial type: TextTextSeries: eBooks on DemandContributions in Mathematical and Computational Sciences: Publisher: Dordrecht : Springer, 2014Description: 1 online resource (499 p.)ISBN: 9783034807159Subject(s): Algebraic fields | Galois theory | Hasse, Helmut, 1898-1979 -- Correspondence | Mathematicians --Austria -- Correspondence | Mathematicians --Germany -- CorrespondenceGenre/Form: Electronic books.Additional physical formats: Print version:: Emil Artin and Helmut Hasse : The Correspondence 1923-1958DDC classification: 512.784 LOC classification: QA247QA29.A768Online resources: Click here to view this ebook.
Contents:
Preface to the Series; Overview; Preface; Contents; List of Figures; Photo Credits; Part I Introduction to the Correspondence; 1. Introduction; Acknowledgements; 2. Emil Artin, his life and his work; 3. Reminiscing Helmut Hasse; 3.1 My first encounter with Helmut Hasse; 3.2 First Version of the Correspondence Artin -Hasse; 3.3 On Hasse and his Biography; 3.4 First Edition of the Correspondence Artin-Hasse; 4. Reciprocity Laws for Power Residues; 5. Class Field Theory; 6. Time Table; Part II The Letters; 1. 1923-1926; 1 09.07.1923, Letter from Artin to Hasse
2 09.07.1923, Postcard from Artin to Hasse3 Date unknown, Letter from Artin to Hasse; 4 Date unknown, Letter from Artin to Hasse; 5 12.07.1923, Postcard from Artin to Hasse; Comments on Letters no. 1-5 (July 1923); 5.1 The Prehistory; 5.2 Hasse's Lecture in Hamburg; 5.3 Artin's Inversion Method; 5.4 Second Supplementary Law; 5.5 General Reciprocity Law; 5.6 The Article on L-Series; 5.7 The Gap 1923-1926; 6 10.02.1926, Letter from Artin to Hasse; Comments on Letter no. 6 dated February 10, 1926; 6.1 Complex Multiplication; 6.2 Topology; 6.3 Eisenstein's reciprocity law; 6.4 Cubic Gauss Sums
6.5 Chebotarev's Article7 10.09.1926, Letter from Artin to Hasse; Comments on letter no. 7, dated Sept. 10, 1926; 7.1 Eisenstein's Method; 2. 1927; 8 17.07.1927, Letter from Artin to Hasse; Comments on Letter no. 8 dated July 17, 1927; 8.1 Artin's Course in 1927; 8.2 The Jacobi Symbol; 8.3 Hasse's Plans for the Annalen; 9 19.07.1927, Letter from Artin to Hasse; Attachment 9 (to the Letter dated 19. 7. 1927); Comments on Letter no. 9; 9.1 The Proof; 9.2 The Method of Abelian Crossing; Abelian Crossing and the Theorem of Kronecker-Weber; 9.3 The Lemma; 9.4 Furtw¨angler's Trick
10 21.07.1927, Letter from Artin to HasseComments on Letter no. 10; 10.1 The s-Formulation; 10.2 Extension of the Jacobi Symbol; 10.3 The Hilbert Symbol; 10.4 The Inversion Factor; 10.5 Part II of Hasse's Report on Class Field Theory; 11 26.07.1927, Letter from Artin to Hasse; Comments on Letter no. 11 from July 26, 1927; 11.1 Primary and Hyperprimary Numbers; 11.2 On the Biquadratic Reciprocity Law; 11.3 Class Number Divisibility; Furtwängler, Chebotarev, Hasse; Publications; 12 29.07.1927, Letter from Artin to Hasse; Comments on Letter no. 12 from July 29, 1927
12.1 The Structure of Class Field TheoryThe Main Theorems of Class Field Theory; Axiomatization: F.K. Schmidt; Emmy Noether; Hasse-Scholz; 13 02.08.1927, Letter from Artin to Hasse; Comments on Letter no. 13; 13.1 On the Principal Ideal Theorem; Transfer; Attempts at a Proof; Furtwängler's Proof; The Further Development; Generalization; 14 06.08.1927, Letter from Artin to Hasse; Comments on Letter no. 14, dated August 6, 1927; 14.1 Relative Units; 14.2 Artin-Schreier and the Beautiful Formula; The Further Development; 15 19.08.1927, Letter from Artin to Hasse
Comments on Letter no. 15, dated Aug. 19, 1927
Summary: This volume consists of the English translations of the letters exchanged between Emil Artin to Helmut Hasse written from 1921 until 1958. The letters are accompanied by extensive comments explaining the mathematical background and giving the information needed for understanding these letters. Most letters deal with class field theory and shed a light on the birth of one of its most profound results: Artin's reciprocity law.
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Preface to the Series; Overview; Preface; Contents; List of Figures; Photo Credits; Part I Introduction to the Correspondence; 1. Introduction; Acknowledgements; 2. Emil Artin, his life and his work; 3. Reminiscing Helmut Hasse; 3.1 My first encounter with Helmut Hasse; 3.2 First Version of the Correspondence Artin -Hasse; 3.3 On Hasse and his Biography; 3.4 First Edition of the Correspondence Artin-Hasse; 4. Reciprocity Laws for Power Residues; 5. Class Field Theory; 6. Time Table; Part II The Letters; 1. 1923-1926; 1 09.07.1923, Letter from Artin to Hasse

2 09.07.1923, Postcard from Artin to Hasse3 Date unknown, Letter from Artin to Hasse; 4 Date unknown, Letter from Artin to Hasse; 5 12.07.1923, Postcard from Artin to Hasse; Comments on Letters no. 1-5 (July 1923); 5.1 The Prehistory; 5.2 Hasse's Lecture in Hamburg; 5.3 Artin's Inversion Method; 5.4 Second Supplementary Law; 5.5 General Reciprocity Law; 5.6 The Article on L-Series; 5.7 The Gap 1923-1926; 6 10.02.1926, Letter from Artin to Hasse; Comments on Letter no. 6 dated February 10, 1926; 6.1 Complex Multiplication; 6.2 Topology; 6.3 Eisenstein's reciprocity law; 6.4 Cubic Gauss Sums

6.5 Chebotarev's Article7 10.09.1926, Letter from Artin to Hasse; Comments on letter no. 7, dated Sept. 10, 1926; 7.1 Eisenstein's Method; 2. 1927; 8 17.07.1927, Letter from Artin to Hasse; Comments on Letter no. 8 dated July 17, 1927; 8.1 Artin's Course in 1927; 8.2 The Jacobi Symbol; 8.3 Hasse's Plans for the Annalen; 9 19.07.1927, Letter from Artin to Hasse; Attachment 9 (to the Letter dated 19. 7. 1927); Comments on Letter no. 9; 9.1 The Proof; 9.2 The Method of Abelian Crossing; Abelian Crossing and the Theorem of Kronecker-Weber; 9.3 The Lemma; 9.4 Furtw¨angler's Trick

10 21.07.1927, Letter from Artin to HasseComments on Letter no. 10; 10.1 The s-Formulation; 10.2 Extension of the Jacobi Symbol; 10.3 The Hilbert Symbol; 10.4 The Inversion Factor; 10.5 Part II of Hasse's Report on Class Field Theory; 11 26.07.1927, Letter from Artin to Hasse; Comments on Letter no. 11 from July 26, 1927; 11.1 Primary and Hyperprimary Numbers; 11.2 On the Biquadratic Reciprocity Law; 11.3 Class Number Divisibility; Furtwängler, Chebotarev, Hasse; Publications; 12 29.07.1927, Letter from Artin to Hasse; Comments on Letter no. 12 from July 29, 1927

12.1 The Structure of Class Field TheoryThe Main Theorems of Class Field Theory; Axiomatization: F.K. Schmidt; Emmy Noether; Hasse-Scholz; 13 02.08.1927, Letter from Artin to Hasse; Comments on Letter no. 13; 13.1 On the Principal Ideal Theorem; Transfer; Attempts at a Proof; Furtwängler's Proof; The Further Development; Generalization; 14 06.08.1927, Letter from Artin to Hasse; Comments on Letter no. 14, dated August 6, 1927; 14.1 Relative Units; 14.2 Artin-Schreier and the Beautiful Formula; The Further Development; 15 19.08.1927, Letter from Artin to Hasse

Comments on Letter no. 15, dated Aug. 19, 1927

This volume consists of the English translations of the letters exchanged between Emil Artin to Helmut Hasse written from 1921 until 1958. The letters are accompanied by extensive comments explaining the mathematical background and giving the information needed for understanding these letters. Most letters deal with class field theory and shed a light on the birth of one of its most profound results: Artin's reciprocity law.

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