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By
David A. Cox
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Bibliographic Detail
Publisher
Wiley-Interscience
Publication date
May 8, 1997
Binding
Paperback
Book category
Adult Non-Fiction
ISBN-13
9780471190790
ISBN-10
0471190799
Dimensions
0.75 by 6.25 by 9.50 in.
Weight
1.15 lbs.
Availability§
Out of Print
Original list price
$139.00
§As reported by publisher
Amazon.com says people who bought this book also bought:
Introduction to Number Theory
Introduction to Number Theory
Summaries and Reviews
(view table of contents)
Amazon.com description: Product Description: 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.
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.
Editions
Hardcover
from Wiley-Interscience (October 1, 1989)
9780471506546 | details & prices | 6.50 × 9.75 × 1.00 in. | 1.55 lbs | List price $122.00
About: Modern number theory began with the work of Euler and Gauss to understand and extend the many unsolved questions left behind by Fermat.
About: Modern number theory began with the work of Euler and Gauss to understand and extend the many unsolved questions left behind by Fermat.
Paperback
2 edition from John Wiley & Sons Inc (April 22, 2013)
9781118390184 | details & prices | 356 pages | 6.00 × 9.50 × 0.75 in. | 1.18 lbs | List price $61.00
The price comparison is for this edition
from Wiley-Interscience (May 8, 1997)
9780471190790 | details & prices | 6.25 × 9.50 × 0.75 in. | 1.15 lbs | List price $139.00
About: Modern number theory began with the work of Euler and Gauss to understand and extend the many unsolved questions left behind by Fermat.
About: Modern number theory began with the work of Euler and Gauss to understand and extend the many unsolved questions left behind by Fermat.
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