|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910299762503321 |
|
|
Autore |
Baumgart Oswald |
|
|
Titolo |
The Quadratic Reciprocity Law : A Collection of Classical Proofs / / by Oswald Baumgart |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2015 |
|
|
|
|
|
|
|
|
|
ISBN |
|
|
|
|
|
|
Edizione |
[1st ed. 2015.] |
|
|
|
|
|
Descrizione fisica |
|
1 online resource (178 p.) |
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
|
|
Soggetti |
|
Number theory |
Number Theory |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Note generali |
|
Description based upon print version of record. |
|
|
|
|
|
|
Nota di bibliografia |
|
Includes bibliographical references and indexes. |
|
|
|
|
|
|
Nota di contenuto |
|
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. |
|
|
|
|
|
|
|
|
Sommario/riassunto |
|
This book is the English translation of Baumgart’s thesis on the early proofs of the quadratic reciprocity law (“Über das quadratische Reciprocitätsgesetz. 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 |
|
|
|
|