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Algebraic Number Theory

e-books in Algebraic Number Theory category

Book cover: Notes on the Theory of Algebraic NumbersNotes on the Theory of Algebraic Numbers
by - arXiv ,
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.
(1860 views)
Book cover: Lectures on Siegel Modular Forms and Representation by Quadratic FormsLectures on Siegel Modular Forms and Representation by Quadratic Forms
by - 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.
(2633 views)
Book cover: Heegner Points and Rankin L-SeriesHeegner Points and Rankin L-Series
by - 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.
(4089 views)

Book cover: Lectures on Topics in Algebraic Number TheoryLectures on Topics in Algebraic Number Theory
by - Indian Institute of Technology, Bombay ,
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.
(5069 views)
Book cover: Lectures on Field Theory and Ramification TheoryLectures on Field Theory and Ramification Theory
by - 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.
(4600 views)
Book cover: An Introduction to Algebraic Number TheoryAn Introduction to Algebraic Number Theory
by - 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.
(4915 views)
Book cover: Introduction to Algebraic Number TheoryIntroduction to Algebraic Number Theory
by - 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...
(6549 views)
Book cover: Complex MultiplicationComplex Multiplication
by ,
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.
(5153 views)
Book cover: Algebraic Number TheoryAlgebraic Number Theory
by ,
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.
(9047 views)
Book cover: A Course In Algebraic Number TheoryA Course In Algebraic Number Theory
by - University of Illinois ,
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.
(9311 views)