Algebraic Number Theory

e-books in Algebraic Number Theory category

Notes on the Theory of Algebraic Numbers
by Steve Wright - arXiv , 2015
This is a series of lecture notes on the elementary theory of algebraic numbers, using only knowledge of a first-semester graduate course in algebra (primarily groups and rings). No prerequisite knowledge of fields is required.
(7254 views)

Lectures on Siegel Modular Forms and Representation by Quadratic Forms
by Y. Kitaoka - Tata Institute of Fundamental Research , 1986
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.
(7902 views)

Heegner Points and Rankin L-Series
by Henri Darmon, Shou-Wu Zhang - Cambridge University Press , 2004
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.
(9547 views)

Lectures on Topics in Algebraic Number Theory
by Sudhir R. Ghorpade - Indian Institute of Technology, Bombay , 2002
These lecture notes give a rapid introduction to some basic aspects of Algebraic Number Theory with as few prerequisites as possible. Topics: Field Extensions; Ring Extensions; Dedekind Domains and Ramification Theory; Class Number and Lattices.
(10671 views)

Lectures on Field Theory and Ramification Theory
by Sudhir R. Ghorpade - Indian Institute of Technology, Bombay , 2008
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.
(10544 views)

An Introduction to Algebraic Number Theory
by F. Oggier - Nanyang Technological University , 2010
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.
(10830 views)

Introduction to Algebraic Number Theory
by William Stein - University of Washington , 2005
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...
(12716 views)

Complex Multiplication
by J. S. Milne , 2006
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.
(11180 views)

Algebraic Number Theory
by J.S. Milne , 2008
Contents: Preliminaries From Commutative Algebra; Rings of Integers; Dedekind Domains; Factorization; The Finiteness of the Class Number; The Unit Theorem; Cyclotomic Extensions; Fermat's Last Theorem; Valuations; Local Fields; Global Fields.
(16796 views)

A Course In Algebraic Number Theory
by Robert B. Ash - University of Illinois , 2003
Basic course in algebraic number theory. It covers the general theory of factorization of ideals in Dedekind domains, the use of Kummer’s theorem, the factorization of prime ideals in Galois extensions, local and global fields, etc.
(16360 views)