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Primes of the Form x2+ny2
Fermat, Class Field Theory, and Complex Multiplication
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Summary
This updated edition introduces class field theory in a well-motivated way, includes elementary treatments of quadratic forms and genus theory, and features new coverage such as the Shimura reciprocity law. It blends accessible explanations with concrete numerical examples and advanced concepts, making it suitable for both reference and coursework.
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Primes of the Form x2+ny2
$12599
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Book Hero Magic created this recommendation. While it's new and still learning, it may not be perfect - your feedback is welcome! IS THIS YOUR NEXT READ?
This book is ideal for undergraduate and graduate students studying number theory or Galois theory, as well as researchers seeking a detailed and accessible reference on the topic. Its clear style suits readers with varied mathematical backgrounds who are interested in the historical and theoretical development of primes in quadratic forms.
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See moreAn exciting approach to the history and mathematics of number theory ... the author s style is totally lucid and very easy to read... the result is indeed a wonderful story.
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Description
An exciting approach to the history and mathematics of number theory
“. . . the author's style is totally lucid and very easy to read . . . the result is indeed a wonderful story.” —Mathematical Reviews
Written in a unique and accessible style for readers of varied mathematical backgrounds, the Second Edition of Primes of the Form p = x2 + ny2 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.
Primes of the Form p = x2 + ny2, Second Edition focuses on addressing the question of when a prime p is of the form x2 + ny2, which serves as the basis for further discussion of various mathematical topics. This updated edition has several new notable features, including:
- A well-motivated introduction to the classical formulation of class field theory
- Illustrations of explicit numerical examples to demonstrate the power of basic theorems in various situations
- An elementary treatment of quadratic forms and genus theory
- Simultaneous treatment of elementary and advanced aspects of number theory
- New coverage of the Shimura reciprocity law and a selection of recent work in an updated bibliography
Primes of the Form p = x2 + ny2, Second Edition is both a useful reference for number theory theorists and an excellent text for undergraduate and graduate-level courses in number and Galois theory.
Series: Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts
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Primes of the Form x2+ny2
An exciting approach to the history and mathematics of number theory “. . . the author's style is totally lucid and very easy to read . . . the result is indeed a wonderful story.” —Mathematical Reviews Written in a unique and accessible style for readers of varied mathematical backgrounds, the Second Edition of Primes of the Form p =...Paperback$12599Unit price /UnavailableAvailableShips in 3-4 weeks
Book Details
INFORMATION
ISBN: 9781118390184
Publisher: John Wiley & Sons Inc
Format: Paperback / softback
Date Published: 17 May 2013
Country: United States
Imprint: John Wiley & Sons Inc
Edition: 2nd edition
Audience: Tertiary education
DIMENSIONS
Spine width: 8.0mm
Width: 150.0mm
Height: 208.0mm
Weight: 544g
Pages: 384
About the Author
DAVID A. COX, PhD, is William J. Walker Professor of Mathematics in the Department of Mathematics at Amherst College. Dr. Cox is the author of Galois Theory, Second Edition, also published by Wiley.
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