Algebraic Number Theory and Related Topics 2008 PDF Download

Author: 中村博昭
Publisher:
ISBN:
Category : Algebraic number theory
Languages : en
Pages : 336

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Author: Pierre Samuel
Publisher: Dover Books on Mathematics
ISBN: 9780486466668
Category : Mathematics
Languages : en
Pages : 0

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Book Description
Algebraic number theory introduces students to new algebraic notions as well as related concepts: groups, rings, fields, ideals, quotient rings, and quotient fields. This text covers the basics, from divisibility theory in principal ideal domains to the unit theorem, finiteness of the class number, and Hilbert ramification theory. 1970 edition.

Author: 中村博昭
Publisher:
ISBN:
Category :
Languages : ja
Pages : 0

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Author: Serge Lang
Publisher: Springer Science & Business Media
ISBN: 146120853X
Category : Mathematics
Languages : en
Pages : 356

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Book Description
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

Author: Henry Berthold Mann
Publisher:
ISBN:
Category : Algebraic number theory
Languages : en
Pages : 190

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Author: Jürgen Neukirch
Publisher: Springer
ISBN: 9783642084737
Category : Mathematics
Languages : en
Pages : 0

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Book Description
This introduction to algebraic number theory discusses the classical concepts from the viewpoint of Arakelov theory. The treatment of class theory is particularly rich in illustrating complements, offering hints for further study, and providing concrete examples. It is the most up-to-date, systematic, and theoretically comprehensive textbook on algebraic number field theory available.

Author: Helmut Koch
Publisher: American Mathematical Soc.
ISBN: 9780821820544
Category : Mathematics
Languages : en
Pages : 390

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Book Description
Algebraic number theory is one of the most refined creations in mathematics. It has been developed by some of the leading mathematicians of this and previous centuries. The primary goal of this book is to present the essential elements of algebraic number theory, including the theory of normal extensions up through a glimpse of class field theory. Following the example set for us by Kronecker, Weber, Hilbert and Artin, algebraic functions are handled here on an equal footing with algebraic numbers. This is done on the one hand to demonstrate the analogy between number fields and function fields, which is especially clear in the case where the ground field is a finite field. On the other hand, in this way one obtains an introduction to the theory of 'higher congruences' as an important element of 'arithmetic geometry'. Early chapters discuss topics in elementary number theory, such as Minkowski's geometry of numbers, public-key cryptography and a short proof of the Prime Number Theorem, following Newman and Zagier. Next, some of the tools of algebraic number theory are introduced, such as ideals, discriminants and valuations. These results are then applied to obtain results about function fields, including a proof of the Riemann-Roch Theorem and, as an application of cyclotomic fields, a proof of the first case of Fermat's Last Theorem. There are a detailed exposition of the theory of Hecke $L$-series, following Tate, and explicit applications to number theory, such as the Generalized Riemann Hypothesis. Chapter 9 brings together the earlier material through the study of quadratic number fields. Finally, Chapter 10 gives an introduction to class field theory. The book attempts as much as possible to give simple proofs. It can be used by a beginner in algebraic number theory who wishes to see some of the true power and depth of the subject. The book is suitable for two one-semester courses, with the first four chapters serving to develop the basic material. Chapters 6 through 9 could be used on their own as a second semester course.

Author: Edwin Weiss
Publisher: Courier Corporation
ISBN: 048615436X
Category : Mathematics
Languages : en
Pages : 308

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Ideal either for classroom use or as exercises for mathematically minded individuals, this text introduces elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global, quadratic, and cyclotomic fields.

Author: M. Ram Murty
Publisher: Springer Science & Business Media
ISBN: 0387221824
Category : Mathematics
Languages : en
Pages : 354

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Book Description
The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject Includes various levels of problems - some are easy and straightforward, while others are more challenging All problems are elegantly solved

Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :

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