The Quadratic Reciprocity Law A Collection of Classical Proofs [Hardcover]

This book is the English translation of Baumgarts thesis on the early proofs of the quadratic reciprocity law (?ber das quadratische Reciprocit?tsgesetz. 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 Baumgarts 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.

Translators 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.

Baumgart collected and analyzed existing proofs of QRL in his 1885 thesis, translated here into English for the first time. & Summing Up: Recommended. (D. V. Feldman, Choice, Vol. 53 (5), January, 2016)

The book has an excellent comparative discussion of many proofs along with historic notes and comments by translator. It contains a vast list of references that are updated. & This excellent book is a necessary one for any number theorist. Every student in the field canl£‹