Number Fields
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Algebraic Number Fields
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Author : Gerald J. Janusz
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Algebraic Number Fields written by Gerald J. Janusz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Algebraic fields categories.
This text presents the basic information about finite dimensional extension fields of the rational numbers, algebraic number fields, and the rings of algebraic integers in them. The important theorems regarding the units of the ring of integers and the class group are proved and illustrated with many examples given in detail. The completion of an algebraic number field at a valuation is discussed in detail and then used to provide economical proofs of global results. The book contains many concrete examples illustrating the computation of class groups, class numbers, and Hilbert class fields. Exercises are provided to indicate applications of the general theory.
Number Fields
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Author : Daniel A. Marcus
language : en
Publisher: Springer
Release Date : 2018-07-05
Number Fields written by Daniel A. Marcus and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-05 with Mathematics categories.
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 in the details, which in many places are left as exercises.
The Theory Of Algebraic Number Fields
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Author : David Hilbert
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
The Theory Of Algebraic Number Fields written by David Hilbert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
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 in the theory, and can be seen as the starting point for all twentieth century investigations into the subject, as well as reciprocity laws and class field theory. This English edition further contains an introduction by F. Lemmermeyer and N. Schappacher.
The Genus Fields Of Algebraic Number Fields
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Author : M. Ishida
language : en
Publisher: Lecture Notes in Mathematics
Release Date : 1976-11
The Genus Fields Of Algebraic Number Fields written by M. Ishida and has been published by Lecture Notes in Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976-11 with Mathematics categories.
Quadratic Number Fields
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Author : Franz Lemmermeyer
language : en
Publisher: Springer
Release Date : 2021-09-19
Quadratic Number Fields written by Franz Lemmermeyer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-19 with Mathematics categories.
This undergraduate textbook provides an elegant introduction to the arithmetic of quadratic number fields, including many topics not usually covered in books at this level. Quadratic fields offer an introduction to algebraic number theory and some of its central objects: rings of integers, the unit group, ideals and the ideal class group. This textbook provides solid grounding for further study by placing the subject within the greater context of modern algebraic number theory. Going beyond what is usually covered at this level, the book introduces the notion of modularity in the context of quadratic reciprocity, explores the close links between number theory and geometry via Pell conics, and presents applications to Diophantine equations such as the Fermat and Catalan equations as well as elliptic curves. Throughout, the book contains extensive historical comments, numerous exercises (with solutions), and pointers to further study. Assuming a moderate background in elementary number theory and abstract algebra, Quadratic Number Fields offers an engaging first course in algebraic number theory, suitable for upper undergraduate students.
A Survey Of Trace Forms Of Algebraic Number Fields
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Author : Pierre E. Conner
language : en
Publisher: World Scientific
Release Date : 1984
A Survey Of Trace Forms Of Algebraic Number Fields written by Pierre E. Conner and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
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 and Sylvester. These notes present the first systematic treatment of the trace form as an object in its own right. Chapter I discusses the trace form of F/Q up to Witt equivalence in the Witt ring W(Q). Special attention is paid to the Witt classes arising from normal extensions F/Q. Chapter II contains a detailed analysis of trace forms over p-adic fields. These local results are applied in Chapter III to prove that a Witt class X in W(Q) is represented by the trace form of an extension F/Q if and only if X has non-negative signature. Chapter IV discusses integral trace forms, obtained by restricting the trace form of F/Q to the ring of algebraic integers in F. When F/Q is normal, the Galois group acts as a group of isometries of the integral trace form. It is proved that when F/Q is normal of prime degree, the integral form is determined up to equivariant integral equivalence by the discriminant of F alone. Chapter V discusses the equivariant Witt theory of trace forms of normal extensions F/Q and Chapter VI relates the trace form of F/Q to questions of ramification in F. These notes were written in an effort to identify central problems. There are many open problems listed in the text. An introduction to Witt theory is included and illustrative examples are discussed throughout.
Cohomology Of Number Fields
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Author : Jürgen Neukirch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-26
Cohomology Of Number Fields written by Jürgen Neukirch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-26 with Mathematics categories.
This second edition is a corrected and extended version of the first. It is a textbook for students, as well as a reference book for the working mathematician, on cohomological topics in number theory. In all it is a virtually complete treatment of a vast array of central topics in algebraic number theory. New material is introduced here on duality theorems for unramified and tamely ramified extensions as well as a careful analysis of 2-extensions of real number fields.
Fourier Analysis On Number Fields
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Author : Dinakar Ramakrishnan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Fourier Analysis On Number Fields written by Dinakar Ramakrishnan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
A modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasising harmonic analysis on topological groups. The main goal is to cover John Tates visionary thesis, giving virtually all of the necessary analytic details and topological preliminaries -- technical prerequisites that are often foreign to the typical, more algebraically inclined number theorist. While most of the existing treatments of Tates thesis are somewhat terse and less than complete, the intent here is to be more leisurely, more comprehensive, and more comprehensible. While the choice of objects and methods is naturally guided by specific mathematical goals, the approach is by no means narrow. In fact, the subject matter at hand is germane not only to budding number theorists, but also to students of harmonic analysis or the representation theory of Lie groups. The text addresses students who have taken a year of graduate-level course in algebra, analysis, and topology. Moreover, the work will act as a good reference for working mathematicians interested in any of these fields.
A Classical Invitation To Algebraic Numbers And Class Fields
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Author : Harvey Cohn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Classical Invitation To Algebraic Numbers And Class Fields written by Harvey Cohn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
"Artin's 1932 Göttingen Lectures on Class Field Theory" and "Connections between Algebrac Number Theory and Integral Matrices"
Analytic Arithmetic In Algebraic Number Fields
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Author : Baruch Z. Moroz
language : en
Publisher: Springer
Release Date : 2006-11-14
Analytic Arithmetic In Algebraic Number Fields written by Baruch Z. Moroz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.