Modern number theory began with the work of Euler and Gauss to understand and extend the many unsolved questions left behind by Fermat. In the course of their investigations, they uncovered new phenomena in need of explanation, which over time led to the discovery of field theory and its intimate connection with complex multiplication. While most texts concentrate on only the elementary or advanced aspects of this story, Primes of the Form x2 + ny2 begins with Fermat and explains how his work ultimately gave birth to ...
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Modern number theory began with the work of Euler and Gauss to understand and extend the many unsolved questions left behind by Fermat. In the course of their investigations, they uncovered new phenomena in need of explanation, which over time led to the discovery of field theory and its intimate connection with complex multiplication. While most texts concentrate on only the elementary or advanced aspects of this story, Primes of the Form x2 + ny2 begins with Fermat and explains how his work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. Further, the book shows how the results of Euler and Gauss can be fully understood only in the context of class field theory. Finally, in order to bring class field theory down to earth, the book explores some of the magnificent formulas of complex multiplication. The central theme of the book is the story of which primes p can be expressed in the form x2 + ny2. An incomplete answer is given using quadratic forms. A better though abstract answer comes from class field theory, and finally, a concrete answer is provided by complex multiplication. Along the way, the reader is introduced to some wonderful number theory. Numerous exercises and examples are included. The book is written to be enjoyed by readers with modest mathematical backgrounds. Chapter 1 uses basic number theory and abstract algebra, while chapters 2 and 3 require Galois theory and complex analysis, respectively.
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Add this copy of Primes of the Form X2 + Ny2: Fermat, Class Field Theory to cart. $40.00, fair condition, Sold by Moe's Books rated 5.0 out of 5 stars, ships from Berkeley, CA, UNITED STATES, published 1989 by John Wiley & Sons, Inc.
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Seller's Description:
Fair. No jacket. Cover is worn and smudged, affecting some legibility. Both the top and bottom edges are dented with small half inch tears. Spine is cocked, but binding is secure. Inside is clean and unmarked.
Add this copy of Primes of the Form X2 + Ny2: Fermat, Class Field Theory to cart. $60.00, good condition, Sold by Moe's Books rated 5.0 out of 5 stars, ships from Berkeley, CA, UNITED STATES, published 1989 by John Wiley & Sons.
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Good. No jacket. Cover is slightly worn, particularly along edges. Spine is shaken but secure. Front free end leaf has previous owner's signature. A few pages have marking in pen, but inside is otherwise clean and unmarked.
Add this copy of Primes of the Form X2+Ny2: Fermat Class Field Theory to cart. $78.68, very good condition, Sold by Fireside Bookshop rated 4.0 out of 5 stars, ships from Stroud, GLOUCESTERSHIRE, UNITED KINGDOM, published 1989 by John Wiley & Sons Inc.
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Very Good in No d/j as Published jacket. Size: 8vo-over 7¾-9¾" tall; Type: Book N.B. Previous owners inscription to inside front cover. No dust jacket. Slight bump to base of spine.
Add this copy of Primes of the Form X2 + Ny2: Fermat, Class Field Theory to cart. $122.63, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 1989 by Wiley-Interscience.
Add this copy of Primes of the Form X2 + Ny2: Fermat, Class Field Theory to cart. $227.52, new condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 1989 by Wiley-Interscience.
