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The quadratic reciprocity law [electronic resource] : a collection of classical proofs

The quadratic reciprocity law [electronic resource] : a collection of classical proofs

자료유형
E-Book(소장)
개인저자
Baumgart, Oswald. Lemmermeyer, Franz, 1962-.
서명 / 저자사항
The quadratic reciprocity law [electronic resource] : a collection of classical proofs / Oswald Baumgart ; edited and translated by Franz Lemmermeyer.
발행사항
Cham :   Springer International Publishing :   Imprint: Birkhäuser,   2015.  
형태사항
1 online resource (xiv, 172 p.) : ill.
ISBN
9783319162836
요약
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 elementary number theory and the history of number theory.
일반주기
Title from e-Book title page.  
내용주기
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.
서지주기
Includes bibliographical references and index.
이용가능한 다른형태자료
Issued also as a book.  
일반주제명
Algebraic number theory.
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020 ▼a 9783319162836
040 ▼a 211009 ▼c 211009 ▼d 211009
041 1 ▼a eng ▼h ger
082 0 4 ▼a 512.74 ▼2 23
084 ▼a 512.74 ▼2 DDCK
090 ▼a 512.74
100 1 ▼a Baumgart, Oswald.
240 1 0 ▼a Über das quadratische Reciprocitätsgesetz. ▼l English
245 1 4 ▼a The quadratic reciprocity law ▼h [electronic resource] : ▼b a collection of classical proofs / ▼c Oswald Baumgart ; edited and translated by Franz Lemmermeyer.
260 ▼a Cham : ▼b Springer International Publishing : ▼b Imprint: Birkhäuser, ▼c 2015.
300 ▼a 1 online resource (xiv, 172 p.) : ▼b ill.
500 ▼a Title from e-Book title page.
504 ▼a Includes bibliographical references and index.
505 0 ▼a 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.
520 ▼a 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 elementary number theory and the history of number theory.
530 ▼a Issued also as a book.
538 ▼a Mode of access: World Wide Web.
650 0 ▼a Algebraic number theory.
700 1 ▼a Lemmermeyer, Franz, ▼d 1962-.
856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=http://dx.doi.org/10.1007/978-3-319-16283-6
945 ▼a KLPA
991 ▼a E-Book(소장)

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