Algebraic number theory / Serge Lang.

Author
Lang, Serge, 1927-2005 [Browse]
Format
Book
Language
English
Εdition
2nd ed.
Published/​Created
New York : Springer-Verlag, ©1994.
Description
xiii, 357 p. : ill. ; 24 cm.

Availability

Copies in the Library

Location Call Number Status Location Service Notes
Lewis Library - Stacks QA247 .L29 1994 Browse related items Request
    Lewis Library - Stacks QA247 .L29 1994 Browse related items Request

      Details

      Subject(s)
      Series
      Graduate texts in mathematics ; 110. [More in this series]
      Summary note
      Publisher Description (unedited publisher data) 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.
      Bibliographic references
      Includes bibliographical references (p. 353-354) and index.
      Contents
      • 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.
      ISBN
      • 0387942254 ((New York))
      • 9780387942254 ((New York))
      • 3540942254 ((Berlin))
      • 9783540942252 ((Berlin))
      LCCN
      93050625
      OCLC
      29667945
      International Article Number
      • 9780387942254
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