The quadratic reciprocity law: a collection of classical proofs
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cham
Birkhäuser Springer
2015
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| Schlagworte: | |
| Online-Zugang: | BTU01 FRO01 TUM01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Beschreibung: | 1 Online-Ressource (XIV, 172 S.) 1 illus |
| ISBN: | 9783319162836 |
| DOI: | 10.1007/978-3-319-16283-6 |
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Datensatz im Suchindex
| _version_ | 1804174754859450368 |
|---|---|
| adam_text | THE QUADRATIC RECIPROCITY LAW
/ BAUMGART, OSWALD
: 2015
TABLE OF CONTENTS / INHALTSVERZEICHNIS
TRANSLATOR’S PREFACE
BAUMGART S THESIS
INTRODUCTION
FIRST PART: 1. FROM FERMAT TO LEGENDRE
2. GAUSS S PROOF BY MATHEMATICAL INDUCTION
3. PROOF BY REDUCTION
4. EISENSTEIN S PROOF USING COMPLEX ANALYSIS
5. PROOFS USING RESULTS FROM CYCLOTOMY
6. PROOFS BASED ON THE THEORY OF QUADRATIC FORMS
7. THE SUPPLEMENTARY LAWS
8. ALGORITHMS FOR DETERMINING THE QUADRATIC CHARACTER
SECOND PART: 9. GAUSS S PROOF BY INDUCTION
10. PROOFS BY REDUCTION
11. EISENSTEIN S PROOFS USING COMPLEX ANALYSIS
12. PROOFS USING RESULTS FROM CYCLOTOMY
13. PROOFS BASED ON THE THEORY OF QUADRATIC FORMS
FINAL COMMENTS
PROOFS OF THE QUADRATIC RECIPROCITY LAW
AUTHOR INDEX
SUBJECT INDEX
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
THE QUADRATIC RECIPROCITY LAW
/ BAUMGART, OSWALD
: 2015
ABSTRACT / INHALTSTEXT
THIS BOOK IS THE ENGLISH TRANSLATION OF BAUMGART’S THESIS ON THE EARLY
PROOFS OF THE QUADRATIC RECIPROCITY LAW (“UEBER DAS QUADRATISCHE
RECIPROCITAETSGESETZ. EINE VERGLEICHENDE DARSTELLUNG DER BEWEISE”),
FIRST PUBLISHED IN 1885. IT IS DIVIDED INTO TWO PARTS. THE FIRST PART
PRESENTS A VERY BRIEF HISTORY OF THE DEVELOPMENT OF NUMBER THEORY UP TO
LEGENDRE, AS WELL AS DETAILED DESCRIPTIONS OF SEVERAL EARLY PROOFS OF
THE QUADRATIC RECIPROCITY LAW. THE SECOND PART HIGHLIGHTS BAUMGART’S
COMPARISONS OF THE PRINCIPLES BEHIND THESE PROOFS. A CURRENT LIST OF ALL
KNOWN PROOFS OF THE QUADRATIC RECIPROCITY LAW, WITH COMPLETE REFERENCES,
IS PROVIDED IN THE APPENDIX. THIS BOOK WILL APPEAL TO ALL READERS
INTERESTED IN ELEMENTARY NUMBER THEORY AND THE HISTORY OF NUMBER THEORY
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-319-16283-6 |
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| spelling | Baumgart, Oswald Verfasser aut Über das quadratische Reciprocitätsgesetz The quadratic reciprocity law a collection of classical proofs Oswald Baumgart Cham Birkhäuser Springer 2015 1 Online-Ressource (XIV, 172 S.) 1 illus txt rdacontent c rdamedia cr rdacarrier Zugl.: Göttingen, Univ., Diss., 1885 u.d.T.: Baumgart, Oswald: Über das quadratische Reciprocitätsgesetz Mathematics Number theory Number Theory Mathematik Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Algebraische Zahlentheorie (DE-588)4001170-7 s 1\p DE-604 Erscheint auch als Druckausgabe 978-3-319-16282-9 https://doi.org/10.1007/978-3-319-16283-6 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028025367&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028025367&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Baumgart, Oswald The quadratic reciprocity law a collection of classical proofs Mathematics Number theory Number Theory Mathematik Algebraische Zahlentheorie (DE-588)4001170-7 gnd |
| subject_GND | (DE-588)4001170-7 (DE-588)4113937-9 |
| title | The quadratic reciprocity law a collection of classical proofs |
| title_alt | Über das quadratische Reciprocitätsgesetz |
| title_auth | The quadratic reciprocity law a collection of classical proofs |
| title_exact_search | The quadratic reciprocity law a collection of classical proofs |
| title_full | The quadratic reciprocity law a collection of classical proofs Oswald Baumgart |
| title_fullStr | The quadratic reciprocity law a collection of classical proofs Oswald Baumgart |
| title_full_unstemmed | The quadratic reciprocity law a collection of classical proofs Oswald Baumgart |
| title_short | The quadratic reciprocity law |
| title_sort | the quadratic reciprocity law a collection of classical proofs |
| title_sub | a collection of classical proofs |
| topic | Mathematics Number theory Number Theory Mathematik Algebraische Zahlentheorie (DE-588)4001170-7 gnd |
| topic_facet | Mathematics Number theory Number Theory Mathematik Algebraische Zahlentheorie Hochschulschrift |
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