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 Series , #116|
|Edition description:||2nd ed.|
|Product dimensions:||6.10(w) x 9.10(h) x 1.00(d)|
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.
Table of Contents
Preface to the First Edition ixPreface to the Second Edition xiNotation xiiiIntroduction 1Chapter One: From Fermat to GaussChapter Two: Class Field TheoryChapter Three: Complex MultiplicationChapter Four: Additional TopicsRefrencesAdditional ReferencesIndex