Primes of the Form x2+ny2
Fermat Class Field Theory and Complex Multiplication
Seiten
1997
|
New edition
John Wiley & Sons Inc (Verlag)
978-0-471-19079-0 (ISBN)
John Wiley & Sons Inc (Verlag)
978-0-471-19079-0 (ISBN)
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This book explains how Fermat's work gave birth to the quadratic reciprocity and the genus of quadratic forms. It goes on to show how the results of Euler and Gauss can be fully understood in the context of classical field theory and explores some of the magnificent formulas of complex multiplication.
Provides a general solution to the question of which primes p can be expressed in the form x + ny . Covered first are the special cases considered by Fermat, which involve only 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 mignificent formulas of complex multiplication.
Provides a general solution to the question of which primes p can be expressed in the form x + ny . Covered first are the special cases considered by Fermat, which involve only 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 mignificent formulas of complex multiplication.
DAVID A. COX is Professor of Mathematics at Amherst College.
FROM FERMAT TO GAUSS.; Fermat, Euler and Quadratic Reciprocity.; Lagrange, Legendre and Quadratic Forms.; Gauss, Composition and Genera.; Cubic and Biquadratic Reciprocity.; CLASS FIELD THEORY.; The Hilbert Class Field and p = x 2 + ny 2 .; The Hilbert Class Field and Genus Theory.; Orders in Imaginary Quadratic Fields.; Class Fields Theory and the Cebotarev Density Theorem.; Ring Class Field and p = x 2 + ny 2 .; COMPLEX MULTIPLICATION.; Elliptic Functions and Complex Multiplication.; Modular Functions and Ring Class Fields.; Modular Functions and Singular j--Invariants.; The Class Equation.; Ellpitic Curves.; References.; Index.
| Erscheint lt. Verlag | 8.5.1997 |
|---|---|
| Reihe/Serie | Pure and Applied Mathematics: A Wiley Series of Texts, Monographs, and Tracts |
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 155 x 236 mm |
| Gewicht | 461 g |
| Einbandart | Paperback |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| ISBN-10 | 0-471-19079-9 / 0471190799 |
| ISBN-13 | 978-0-471-19079-0 / 9780471190790 |
| Zustand | Neuware |
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