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Original Essays | September 17, 2014

Merritt Tierce: IMG Has My Husband Read It?



My first novel, Love Me Back, was published on September 16. Writing the book took seven years, and along the way three chapters were published in... Continue »
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    Love Me Back

    Merritt Tierce 9780385538077

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Applied Mathematical Sciences #110: Algebraic Number Theory

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Applied Mathematical Sciences #110: Algebraic Number Theory Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

This is a 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. "Lang's books are always of great value for the graduate student and the research mathematician. This updated edition of Algebraic number theory is no exception."---MATHEMATICAL REVIEWS

Table of Contents

Part I: General Basic Theory: Algebraic Integers. Completions. The Different and Discriminant. Cyclotomic Fields. Paralellotopes. The Ideal Function. Ideles and Adeles. Elementary Properties of the Zeta Function and L-series.- Part II: Class Field Theory: Norm Index Computations. The Artin Symbol, Reciprocity Law, and Class Field Theory. The Existence Theorem and Local Class Field Theory. L-series Again.- Part III: Analytic Theory: 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.- Bibliography.- Index.

Product Details

ISBN:
9780387942254
Author:
Lang, Serge
Publisher:
Springer
Location:
New York, NY
Subject:
Number Theory
Subject:
Algebraic number theory
Subject:
Mathematics-Number Theory
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Copyright:
Edition Number:
2
Edition Description:
1994. Corr. 3rd
Series:
Applied Mathematical Sciences
Series Volume:
110
Publication Date:
19940624
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
370
Dimensions:
235 x 155 mm 1550 gr

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Applied Mathematical Sciences #110: Algebraic Number Theory New Hardcover
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Product details 370 pages Springer-Verlag - English 9780387942254 Reviews:
"Synopsis" by , This is a 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. "Lang's books are always of great value for the graduate student and the research mathematician. This updated edition of Algebraic number theory is no exception."---MATHEMATICAL REVIEWS
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