Classical theory of algebraic numbers
著者
書誌事項
Classical theory of algebraic numbers
（Universitext）
Springer, c2001
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注記
Rev. ed. of: Algebraic numbers. 1972
Includes bibliographical references (p. 665-672) and indexes
内容説明・目次
内容説明
The exposition of the classical theory of algebraic numbers is clear and thorough, and there is a large number of exercises as well as worked out numerical examples. A careful study of this book will provide a solid background to the learning of more recent topics.
目次
* Unique Factorization Domains, Ideals, Principal Ideal Domains * Commutative Fields * Residue Classes * Quadratic Residues * Algebraic Integers * Integral Basis, Discriminant * The Decomposition of Ideals * The Norm and Classes of Ideals * Estimates for the Discriminant * Units * Extension of Ideals * Algebraic Interlude * The Relative Trace, Norm, Discriminant and Different * The Decomposition of Prime Ideals in Galois Extensions * Complements and Miscellaneous Numerical Examples * Local Methods for Cyclotomic Fields * Bernoulli Numbers * Fermat's Last Theorem for Regular Prime Exponents * More on Cyclotomic Extensions * Characters and Gaussian Sums * Zeta-Functions and L-Series * The Dedekind Zeta- Function * Primes in Arithmetic Progressions * The Frobenius Automorphism and the Splitting of Prime Ideals * Class Number of Quadratic Fields * Class Number of Cyclotomic Fields * Miscellaneous Results about the Class Number of Cyclotomic Fields
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