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135   $aur|n|---|||||
181   $ctxt
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183   $acr
200 14$aThe Quadratic Reciprocity Law $eA Collection of Classical Proofs /$fby Oswald Baumgart
205   $a1st ed. 2015.
210  1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2015.
215   $a1 online resource (178 p.)
300   $aDescription based upon print version of record.
311   $a3-319-16282-9 
320   $aIncludes bibliographical references and indexes.
327   $aTranslator?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.
330   $aThis 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.
606   $aNumber theory
606   $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001
615  0$aNumber theory.
615 14$aNumber Theory.
676   $a510
676   $a512.7
700   $aBaumgart$b Oswald$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755574
906   $aBOOK
912   $a9910299762503321
996   $aThe Quadratic Reciprocity Law$92499544
997   $aUNINA