Algebraic number theory

by Lang, Serge

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Title Statements

Full title :Algebraic number theory / Serge Lang.

Summary

This is a corrected printing of the second edition of Lang's well-known textbook. It covers all of the basic material of classical algebraic number theory, giving the student the background necessary for the study of further topics in algebraic number theory, such as cyclotomic fields, or modular forms. Part I introduces some of the basic ideas of the theory: number fields, ideal classes, ideles and adeles, and zeta functions. It also contains a version of a Riemann-Roch theorem in number fields, proved by Lang in the very first version of the book in the sixties. This version can now be seen as a precursor of Arakelov theory. Part II covers class field theory, and Part III is devoted to analytic methods, including an exposition of Tate's thesis, the Brauer-Siegel theorem, and Weil's explicit formulas. The second edition contains corrections, as well as several additions to the previous edition, and the last chapter on explicit formulas has been rewritten.

Edition Statements

Publication Date:©1994.
Edition:2nd ed

Publication Statements

Publisher(s):Springer-Verlag
Place of Publication:New York
Language:eng
Publication Date:©1994.

The Physical Object

Description:1 online resource (xiii, 357 pages) : : illustrations

Edition Identifiers

ISBN:9781461208532, 146120853X, 9781461269229, 1461269229
DOI:10.1007/978-1-4612-0853-2
oclc:ocn681192627
LC Classification:QA247
Dewey Decimal:512/.74

Algebraic integers -- Completions -- The different and discriminant -- Cyclotomic fields -- Parallelotopes -- The ideal function -- Ideles and adeles -- Elementary properties of the zeta function and L-series -- Norm index computations -- The Artin symbol, reciprocity law, and class field theory -- The existence theorem and local class field theory -- L-series again -- Functional equation of the zeta function, Hecke's proof -- Functional equation, Tate's thesis -- Density of primes and Tauberian theorem -- The Brauer-Siegel theorem -- Explicit formulas.