Basic Number Theory (Grundlehren der mathematischen Wissenschaften)

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9783540586555: Basic Number Theory (Grundlehren der mathematischen Wissenschaften)
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From the reviews: "L.R. Shafarevich showed me the first edition [...] and said that this book will be from now on the book about class field theory. In fact it is by far the most complete treatment of the main theorems of algebraic number theory, including function fields over finite constant fields, that appeared in book form." Zentralblatt MATH

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About the Author:

Biography of André Weil

André Weil was born on May 6, 1906 in Paris. After studying mathematics at the École Normale Supérieure and receiving a doctoral degree from the University of Paris in 1928, he held professorial positions in India, France, the United States and Brazil before being appointed to the Institute for Advanced Study, Princeton in 1958, where he remained until he died on August 6, 1998.

André Weil's work laid the foundation for abstract algebraic geometry and the modern theory of abelian varieties. A great deal of his work was directed towards establishing the links between number theory and algebraic geometry and devising modern methods in analytic number theory. Weil was one of the founders, around 1934, of the group that published, under the collective name of  N. Bourbaki, the highly influential multi-volume treatise Eléments de mathématique.

Review:

"L.R. Shafarevich showed me the first edition in autumn 1967 in Moscow and said that this book will be from now on the book about class field theory. In fact it is by far the most complete treatment of the main theorems of algebraic number theory, including function fields over finite constant fields, that appeared in book form. The theory is presented in a uniform way starting with topological fields and Haar measure on related groups, and it includes not only class field theory but also the theory of simple algebras over local and global fields, which serves as a foundation for class field theory. The spirit of the book is the idea that all this is asic number theory' about which elevates the edifice of the theory of automorphic forms and representations and other theories.
To develop this basic number theory on 312 pages efforts a maximum of concentration on the main features. So, there is absolutely no example which illustrates the rather abstract material and brings it nearer to the heart of the reader.
This is not a book for beginners. This book is written in the spirit of the early forties and just this makes it a valuable source of information for everyone who is working about problems related to number and function fields."
Zentralblatt MATH, 823

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Other Popular Editions of the Same Title

9783540038313: Basic Number Theory (Grundlehren Der Mathematischen Wissenschaften Volume 144)

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ISBN 10:  3540038310 ISBN 13:  9783540038313
Publisher: Springer, 1967
Hardcover

9780387586557: Basic Number Theory

Spring..., 1995
Softcover

9780387069357: Basic Number Theory (Grundlehren Der Mathematischen Wissenschaften Volume 144)

Springer, 1985
Hardcover

9783540061779: Basic Number Theory. (Grundlehren Der Mathematischen Wissenschaften (Springer Hardcover))

Springer, 1973
Hardcover

9780387061771: Basic number theory (Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen)

Spring..., 1973
Hardcover

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