Introduction to Algebraic Number Theory
by William Stein
Publisher: University of Washington 2005
Number of pages: 140
Description:
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; Decomposition and inertia groups, Frobenius elements; Ramification; Discriminant and different; Quadratic and biquadratic fields; etc.
Download or read it online for free here:
Download link
(820KB, PDF)
Similar books
Lectures on Field Theory and Ramification Theoryby 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.
(6436 views)
Lectures on Siegel Modular Forms and Representation by Quadratic Formsby 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.
(4286 views)
Complex Multiplicationby 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.
(6741 views)
Heegner Points and Rankin L-Seriesby 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.
(6025 views)