Screen LibraryThe quadratic reciprocity law : a collection of classical proofs /
This book is the English translation of Baumgart's thesis on the early proofs of the quadratic reciprocity law, 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 description...
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| Group Author: | |
| Published: |
Birkhäuser,
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| Publisher Address: | Cham : |
| Publication Dates: | [2015] |
| Literature type: | Book |
| Language: | English |
| Subjects: | |
| Summary: |
This book is the English translation of Baumgart's thesis on the early proofs of the quadratic reciprocity law, 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. |
| Carrier Form: | xiv, 172 pages : illustrations ; 24 cm |
| Bibliography: | Includes bibliographical references (pages 163-166) and indexes. |
| ISBN: |
9783319162829 3319162829 |
| Index Number: | QA242 |
| CLC: | O156.2 |
| Call Number: | O156.2/B348 |
| Contents: | Translator's preface -- 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. |