Algebraic Number Fields PDF Books

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Algebraic Number Fields

Algebraic Number Fields
Author: Gerald J. Janusz
Publisher: American Mathematical Soc.
ISBN: 0821804294
Size: 76.37 MB
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The book is directed toward students with a minimal background who want to learn class field theory for number fields. The only prerequisite for reading it is some elementary Galois theory. The first three chapters lay out the necessary background in number fields, such as the arithmetic of fields, Dedekind domains, and valuations. The next two chapters discuss class field theory for number fields. The concluding chapter serves as an illustration of the concepts introduced in previous chapters. In particular, some interesting calculations with quadratic fields show the use of the norm residue symbol. For the second edition the author added some new material, expanded many proofs, and corrected errors found in the first edition. The main objective, however, remains the same as it was for the first edition: to give an exposition of the introductory material and the main theorems about class fields of algebraic number fields that would require as little background preparation as possible. Janusz's book can be an excellent textbook for a year-long course in algebraic number theory; the first three chapters would be suitable for a one-semester course. It is also very suitable for independent study.
Algebraic Number Fields
Language: en
Pages: 276
Authors: Gerald J. Janusz
Categories: Mathematics
Type: BOOK - Published: 1996 - Publisher: American Mathematical Soc.
The book is directed toward students with a minimal background who want to learn class field theory for number fields. The only prerequisite for reading it is some elementary Galois theory. The first three chapters lay out the necessary background in number fields, such as the arithmetic of fields, Dedekind
The Genus Fields of Algebraic Number Fields
Language: en
Pages: 122
Authors: M. Ishida
Categories: Mathematics
Type: BOOK - Published: 2006-12-08 - Publisher: Springer
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Analytic Arithmetic in Algebraic Number Fields
Language: en
Pages: 180
Authors: Baruch Z. Moroz
Categories: Mathematics
Type: BOOK - Published: 2006-11-14 - Publisher: Springer
Books about Analytic Arithmetic in Algebraic Number Fields
Number Fields
Language: en
Pages: 203
Authors: Daniel A. Marcus
Categories: Mathematics
Type: BOOK - Published: 2018-07-05 - Publisher: Springer
Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, pedestrian manner. It therefore avoids local methods and presents proofs in a way that highlights the important parts of the arguments. Readers are assumed to be able to fill
The Theory of Algebraic Number Fields
Language: en
Pages: 351
Authors: David Hilbert
Categories: Mathematics
Type: BOOK - Published: 2013-03-14 - Publisher: Springer Science & Business Media
A translation of Hilberts "Theorie der algebraischen Zahlkörper" best known as the "Zahlbericht", first published in 1897, in which he provides an elegantly integrated overview of the development of algebraic number theory up to the end of the nineteenth century. The Zahlbericht also provided a firm foundation for further research
Algebraic Number Fields
Language: en
Pages: 704
Authors: Albrecht Fröhlich, London Mathematical Society
Categories: 2 L-functions
Type: BOOK - Published: 1977 - Publisher:
Books about Algebraic Number Fields
The Genus Fields of Algebraic Number Fields
Language: en
Pages: 115
Authors: Makoto Ishida
Categories: Algebraic fields
Type: BOOK - Published: 1976-01-01 - Publisher: Springer
Books about The Genus Fields of Algebraic Number Fields
Galois Cohomology of Algebraic Number Fields
Language: en
Pages: 145
Authors: Klaus Haberland, Helmut Koch, Thomas Zink
Categories: Algebraic fields
Type: BOOK - Published: 1978 - Publisher:
Books about Galois Cohomology of Algebraic Number Fields
Diophantine Equations and Inequalities in Algebraic Number Fields
Language: en
Pages: 170
Authors: Yuan Wang
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media
The circle method has its genesis in a paper of Hardy and Ramanujan (see [Hardy 1])in 1918concernedwiththepartitionfunction andtheproblemofrep resenting numbers as sums ofsquares. Later, in a series of papers beginning in 1920entitled "some problems of'partitio numerorum''', Hardy and Littlewood (see [Hardy 1]) created and developed systematically a new analytic method,
A Survey of Trace Forms of Algebraic Number Fields
Language: en
Pages: 316
Authors: Pierre E. Conner, R. Perlis
Categories: Mathematics
Type: BOOK - Published: 1984 - Publisher: World Scientific
Every finite separable field extension F/K carries a canonical inner product, given by trace(xy). This symmetric K-bilinear form is the trace form of F/K.When F is an algebraic number field and K is the field Q of rational numbers, the trace form goes back at least 100 years to Hermite