The Quadratic Reciprocity Law A Collection of Classical Proofs /

• Main Author: Baumgart, Oswald (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2015.
• Subjects: Mathematics.; Number theory.; Number Theory.

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 histor...

Table of Contents:

• 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.