Buch, Englisch, 682 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 1221 g
Reihe: Universitext
Buch, Englisch, 682 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 1221 g
Reihe: Universitext
ISBN: 978-0-387-95070-9
Verlag: Springer
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.
Zielgruppe
Graduate
Autoren/Hrsg.
Weitere Infos & Material
Unique Factorization Domains, Ideals, and Principal Ideal Domains.- Commutative Fields.- One.- Residue Classes.- Quadratic Residues.- Two.- 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.- The Fundamental Theorem of Abelian Extensions.- Complements and Miscellaneous Numerical Examples.- Three.- Local Methods for Cyclotomic Fields.- Bernoulli Numbers.- Fermat’s Last Theorem for Regular Prime Exponents.- More on Cyclotomic Extensions.- Four.- 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 Numbers of Quadratic Fields.- Class Number of Cyclotomic Fields.- Miscellaneous Results About the Class Number of Quadratic Fields.- Miscellaneous Results About the Class Number of Cyclotomic Fields.
