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Algebraic Number Theory and Class Field TheoryAlgebraic Number Theory and Class Field Theory
by Holden Lee - MIT , 2012
Contents: Rings of integers; Ideal factorization; The class group; The algebra of quadratic forms; Units in number fields; Cyclotomic fields; Valuations and completions; Local and global fields; Ramification; Class Field Theory; Group homology...
(1256 views)

Lectures on Siegel Modular Forms and Representation by Quadratic FormsLectures 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.
(1182 views)

Heegner Points and Rankin L-SeriesHeegner 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.
(1828 views)

Lectures on Topics in Algebraic Number TheoryLectures 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.
(2126 views)

Lectures on Field Theory and Ramification TheoryLectures 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.
(2687 views)

An Introduction to Algebraic Number TheoryAn 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.
(2923 views)

Introduction to Algebraic Number TheoryIntroduction 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...
(3741 views)

Complex MultiplicationComplex 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.
(3405 views)

Algebraic Number TheoryAlgebraic 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.
(6931 views)

A Course In Algebraic Number TheoryA 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.
(11987 views)