Topics covered in this volume include: quadratic reciprocity, quadratic forms, genus theory, cubic and biquadratic reciprocity, class field theory, orders in quadratic fields, elliptic functions, modular functions and complex multiplication. The central question of when a prime p is of the form x2 + ny2 is covered by the author at both elementary and advanced level, thus making the book accessible to a wide range of readers.
Sprache
Verlagsort
Verlagsgruppe
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Für höhere Schule und Studium
Für Beruf und Forschung
Illustrationen
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ISBN-13
978-0-471-50654-6 (9780471506546)
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Schweitzer Klassifikation
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 = x2 + ny2. The Hilbert Class Field and Genus Theory. Orders in Imaginary Quadratic Fields. Class Field Theory and the ebotarev Density Theorem. Ring Class Field and p = x2 + ny2. 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.
