{"product_id":"9781118390184","title":"Primes of the Form x2+ny2 Fermat, Class Field Theory, and Complex Multiplication","description":"\u003ch3\u003ePure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts\u003c\/h3\u003e\u003ch1\u003ePrimes of the Form x2+ny2\u003c\/h1\u003e\u003ch2\u003eFermat, Class Field Theory, and Complex Multiplication\u003c\/h2\u003e\u003ch3\u003eDavid A. Cox\u003c\/h3\u003e\u003cdiv\u003e\u003cb\u003eMathematics \/ Number Theory\u003c\/b\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\n\u003cp\u003e\u003cb\u003eAn exciting approach to the history and mathematics of number theory\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e“. . . the author’s style is totally lucid and very easy to read . . .the result is indeed a wonderful story.” \u003ci\u003e—Mathematical Reviews\u003cbr\u003e \u003cbr\u003e \u003c\/i\u003eWritten in a unique and accessible style for readers of varied mathematical backgrounds, the \u003ci\u003eSecond Edition\u003c\/i\u003e of \u003ci\u003ePrimes of the Form p = x\u003csub\u003e\u003ci\u003e2\u003c\/i\u003e\u003c\/sub\u003e\u003c\/i\u003e\u003ci\u003e+ ny\u003c\/i\u003e\u003csub\u003e\u003ci\u003e2\u003c\/i\u003e\u003c\/sub\u003e details the history behind how Pierre de Fermat’s work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. The book also illustrates how results of Euler and Gauss can be fully understood only in the context of class field theory, and in addition, explores a selection of the magnificent formulas of complex multiplication.\u003c\/p\u003e \u003cp\u003e\u003ci\u003ePrimes of the Form p = x\u003c\/i\u003e\u003csub\u003e\u003ci\u003e2\u003c\/i\u003e\u003c\/sub\u003e \u003ci\u003e+ ny\u003c\/i\u003e\u003csub\u003e\u003ci\u003e2\u003c\/i\u003e\u003c\/sub\u003e\u003ci\u003e, Second Edition\u003c\/i\u003e focuses on addressing the question of when a prime \u003ci\u003ep\u003c\/i\u003e is of the form \u003ci\u003ex\u003c\/i\u003e\u003csub\u003e\u003ci\u003e2\u003c\/i\u003e\u003c\/sub\u003e \u003ci\u003e+ ny\u003c\/i\u003e\u003csub\u003e\u003ci\u003e2\u003c\/i\u003e\u003c\/sub\u003e\u003ci\u003e,\u003c\/i\u003e which serves as the basis for further discussion of various mathematical topics. This updated edition has several new notable features, including:\u003c\/p\u003e \u003cp\u003e• A well-motivated introduction to the classical formulation of class field theory\u003c\/p\u003e \u003cp\u003e• Illustrations of explicit numerical examples to demonstrate the power of basic theorems in various situations\u003c\/p\u003e \u003cp\u003e• An elementary treatment of quadratic forms and genus theory\u003c\/p\u003e \u003cp\u003e• Simultaneous treatment of elementary and advanced aspects of number theory\u003c\/p\u003e \u003cp\u003e• New coverage of the Shimura reciprocity law and a selection of recent work in an updated bibliography\u003c\/p\u003e \u003cp\u003e\u003ci\u003ePrimes of the Form p = x\u003c\/i\u003e\u003csub\u003e\u003ci\u003e2\u003c\/i\u003e\u003c\/sub\u003e \u003ci\u003e+ ny\u003c\/i\u003e\u003csub\u003e\u003ci\u003e2\u003c\/i\u003e\u003c\/sub\u003e\u003ci\u003e, Second Edition\u003c\/i\u003e is both a useful reference for number theory theorists and an excellent text for undergraduate and graduate-level courses in number and Galois theory.\u003c\/p\u003e\n\u003c\/div\u003e\u003cdiv\u003e \u003cp\u003e\u003cb\u003eDAVID A. COX,\u003c\/b\u003e \u003cb\u003ePhD,\u003c\/b\u003e is William J. Walker Professor of Mathematics in the Department of Mathematics at Amherst College. Dr. Cox is the author of \u003ci\u003eGalois Theory, Second Edition,\u003c\/i\u003e also published by Wiley.\u003c\/p\u003e \u003c\/div\u003e\u003cbr\u003e\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublication Date: \u003c\/td\u003e\n\u003ctd\u003e29 April 2013\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublisher: \u003c\/td\u003e\n\u003ctd\u003eWiley\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eImprint: \u003c\/td\u003e\n\u003ctd\u003eWiley\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eISBN-13: \u003c\/td\u003e\n\u003ctd\u003e9781118390184\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eFormat: \u003c\/td\u003e\n\u003ctd\u003ePaperback \/ softback\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePage Count: \u003c\/td\u003e\n\u003ctd\u003e384\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eWeight (oz): \u003c\/td\u003e\n\u003ctd\u003e19.2\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":44378821263500,"sku":"9781118390184","price":61.16,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9781118390184.jpg?v=1780174945","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9781118390184","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}