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 Sudhir R. Ghorpade - Indian Institute of Technology, Bombay
These are notes of a series of lectures, aimed at covering the essentials of Field Theory and Ramification Theory as may be needed for local and global class field theory. Included are the two sections on cyclic extensions and abelian extensions.
by Henri Darmon, Shou-Wu Zhang - Cambridge University Press
This volume has the Gross-Zagier formula and its avatars as a common unifying theme. It covers the theory of complex multiplication, automorphic forms, the Rankin-Selberg method, arithmetic intersection theory, Iwasawa theory, and other topics.