## 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.

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**2827**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.

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**3685**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.

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**5320**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.

(

**6196**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.

(

**5773**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.

(

**6161**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...

(

**7618**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.

(

**6067**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.

(

**10247**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 Kummerâ€™s theorem, the factorization of prime ideals in Galois extensions, local and global fields, etc.

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**10382**views)