Classical Theory of Algebraic Numbers

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.

Inhalt

• 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