A Course In Algebraic Number Theory
by Robert B. Ash
Publisher: University of Illinois 2003
This is a text for a basic course in algebraic number theory, written to provide reasonable coverage for a one-semester course. The text covers the general theory of factorization of ideals in Dedekind domains, detailed calculations illustrating the use of Kummer’s theorem, the factorization of prime ideals in Galois extensions, local and global fields, etc. A standard graduate course in algebra is assumed as prerequisite.
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by J. S. Milne
These are preliminary notes for a modern account of the theory of complex multiplication. The reader is expected to have a good knowledge of basic algebraic number theory, and basic algebraic geometry, including abelian varieties.
by Y. Kitaoka - Tata Institute of Fundamental Research
This book is concerned with the problem of representation of positive definite quadratic forms by other such forms. From the table of contents: Preface; Fourier Coefficients of Siegel Modular Forms; Arithmetic of Quadratic Forms.
by William Stein - University of Washington
Topics in this book: Rings of integers of number fields; Unique factorization of ideals in Dedekind domains; Structure of the group of units of the ring of integers; Finiteness of the group of equivalence classes of ideals of the ring of integers...
by F. Oggier - Nanyang Technological University
Contents: Algebraic numbers and algebraic integers (Rings of integers, Norms and Traces); Ideals (Factorization and fractional ideals, The Chinese Theorem); Ramification theory; Ideal class group and units; p-adic numbers; Valuations; p-adic fields.