Quadratic Number Fields

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Quadratic Number Fields

Author : Franz Lemmermeyer
Publisher : Springer Nature
ISBN 13 : 3030786528
Total Pages : 348 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Quadratic Number Fields by : Franz Lemmermeyer

Download or read book Quadratic Number Fields written by Franz Lemmermeyer and published by Springer Nature. This book was released on 2021-09-18 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic Theory of Quadratic Numbers

Author : Mak Trifković
Publisher : Springer Science & Business Media
ISBN 13 : 1461477174
Total Pages : 206 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Algebraic Theory of Quadratic Numbers by : Mak Trifković

Download or read book Algebraic Theory of Quadratic Numbers written by Mak Trifković and published by Springer Science & Business Media. This book was released on 2013-09-14 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: By focusing on quadratic numbers, this advanced undergraduate or master’s level textbook on algebraic number theory is accessible even to students who have yet to learn Galois theory. The techniques of elementary arithmetic, ring theory and linear algebra are shown working together to prove important theorems, such as the unique factorization of ideals and the finiteness of the ideal class group. The book concludes with two topics particular to quadratic fields: continued fractions and quadratic forms. The treatment of quadratic forms is somewhat more advanced than usual, with an emphasis on their connection with ideal classes and a discussion of Bhargava cubes. The numerous exercises in the text offer the reader hands-on computational experience with elements and ideals in quadratic number fields. The reader is also asked to fill in the details of proofs and develop extra topics, like the theory of orders. Prerequisites include elementary number theory and a basic familiarity with ring theory.

Quadratic Number Theory: An Invitation to Algebraic Methods in the Higher Arithmetic

Author : J. L. Lehman
Publisher : American Mathematical Soc.
ISBN 13 : 1470447371
Total Pages : 394 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Quadratic Number Theory: An Invitation to Algebraic Methods in the Higher Arithmetic by : J. L. Lehman

Download or read book Quadratic Number Theory: An Invitation to Algebraic Methods in the Higher Arithmetic written by J. L. Lehman and published by American Mathematical Soc.. This book was released on 2019-02-13 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quadratic Number Theory is an introduction to algebraic number theory for readers with a moderate knowledge of elementary number theory and some familiarity with the terminology of abstract algebra. By restricting attention to questions about squares the author achieves the dual goals of making the presentation accessible to undergraduates and reflecting the historical roots of the subject. The representation of integers by quadratic forms is emphasized throughout the text. Lehman introduces an innovative notation for ideals of a quadratic domain that greatly facilitates computation and he uses this to particular effect. The text has an unusual focus on actual computation. This focus, and this notation, serve the author's historical purpose as well; ideals can be seen as number-like objects, as Kummer and Dedekind conceived of them. The notation can be adapted to quadratic forms and provides insight into the connection between quadratic forms and ideals. The computation of class groups and continued fraction representations are featured—the author's notation makes these computations particularly illuminating. Quadratic Number Theory, with its exceptionally clear prose, hundreds of exercises, and historical motivation, would make an excellent textbook for a second undergraduate course in number theory. The clarity of the exposition would also make it a terrific choice for independent reading. It will be exceptionally useful as a fruitful launching pad for undergraduate research projects in algebraic number theory.

Rational Quadratic Forms

Author : J. W. S. Cassels
Publisher : Courier Dover Publications
ISBN 13 : 0486466701
Total Pages : 429 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Rational Quadratic Forms by : J. W. S. Cassels

Download or read book Rational Quadratic Forms written by J. W. S. Cassels and published by Courier Dover Publications. This book was released on 2008-08-08 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploration of quadratic forms over rational numbers and rational integers offers elementary introduction. Covers quadratic forms over local fields, forms with integral coefficients, reduction theory for definite forms, more. 1968 edition.

The Algebraic Theory of Quadratic Forms

Author : Tsit-Yuen Lam
Publisher : Addison-Wesley
ISBN 13 : 9780805356663
Total Pages : 344 pages
Book Rating : 4.3/5 (566 download)

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Book Synopsis The Algebraic Theory of Quadratic Forms by : Tsit-Yuen Lam

Download or read book The Algebraic Theory of Quadratic Forms written by Tsit-Yuen Lam and published by Addison-Wesley. This book was released on 1980 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Theory of Algebraic Number Fields

Author : David Hilbert
Publisher : Springer Science & Business Media
ISBN 13 : 3662035456
Total Pages : 360 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis The Theory of Algebraic Number Fields by : David Hilbert

Download or read book The Theory of Algebraic Number Fields written by David Hilbert and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Number Theory in the Quadratic Field with Golden Section Unit

Author : Fred Wayne Dodd
Publisher :
ISBN 13 :
Total Pages : 168 pages
Book Rating : 4.:/5 (41 download)

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Book Synopsis Number Theory in the Quadratic Field with Golden Section Unit by : Fred Wayne Dodd

Download or read book Number Theory in the Quadratic Field with Golden Section Unit written by Fred Wayne Dodd and published by . This book was released on 1983 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Number Fields

Author : Daniel A. Marcus
Publisher : Springer
ISBN 13 : 3319902334
Total Pages : 213 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Number Fields by : Daniel A. Marcus

Download or read book Number Fields written by Daniel A. Marcus and published by Springer. This book was released on 2018-07-05 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Genus Fields of Algebraic Number Fields

Author : M. Ishida
Publisher : Springer
ISBN 13 : 3540375538
Total Pages : 123 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis The Genus Fields of Algebraic Number Fields by : M. Ishida

Download or read book The Genus Fields of Algebraic Number Fields written by M. Ishida and published by Springer. This book was released on 2006-12-08 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: a

Jacobi Forms, Finite Quadratic Modules and Weil Representations over Number Fields

Author : Hatice Boylan
Publisher : Springer
ISBN 13 : 3319129163
Total Pages : 150 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Jacobi Forms, Finite Quadratic Modules and Weil Representations over Number Fields by : Hatice Boylan

Download or read book Jacobi Forms, Finite Quadratic Modules and Weil Representations over Number Fields written by Hatice Boylan and published by Springer. This book was released on 2014-12-05 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new theory of Jacobi forms over totally real number fields introduced in this monograph is expected to give further insight into the arithmetic theory of Hilbert modular forms, its L-series, and into elliptic curves over number fields. This work is inspired by the classical theory of Jacobi forms over the rational numbers, which is an indispensable tool in the arithmetic theory of elliptic modular forms, elliptic curves, and in many other disciplines in mathematics and physics. Jacobi forms can be viewed as vector valued modular forms which take values in so-called Weil representations. Accordingly, the first two chapters develop the theory of finite quadratic modules and associated Weil representations over number fields. This part might also be interesting for those who are merely interested in the representation theory of Hilbert modular groups. One of the main applications is the complete classification of Jacobi forms of singular weight over an arbitrary totally real number field.

Quadratics

Author : Richard A. Mollin
Publisher : CRC Press
ISBN 13 : 1351420763
Total Pages : 422 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Quadratics by : Richard A. Mollin

Download or read book Quadratics written by Richard A. Mollin and published by CRC Press. This book was released on 2018-04-27 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first thing you will find out about this book is that it is fun to read. It is meant for the browser, as well as for the student and for the specialist wanting to know about the area. The footnotes give an historical background to the text, in addition to providing deeper applications of the concept that is being cited. This allows the browser to look more deeply into the history or to pursue a given sideline. Those who are only marginally interested in the area will be able to read the text, pick up information easily, and be entertained at the same time by the historical and philosophical digressions. It is rich in structure and motivation in its concentration upon quadratic orders. This is not a book that is primarily about tables, although there are 80 pages of appendices that contain extensive tabular material (class numbers of real and complex quadratic fields up to 104; class group structures; fundamental units of real quadratic fields; and more!). This book is primarily a reference book and graduate student text with more than 200 exercises and a great deal of hints! The motivation for the text is best given by a quote from the Preface of Quadratics: "There can be no stronger motivation in mathematical inquiry than the search for truth and beauty. It is this author's long-standing conviction that number theory has the best of both of these worlds. In particular, algebraic and computational number theory have reached a stage where the current state of affairs richly deserves a proper elucidation. It is this author's goal to attempt to shine the best possible light on the subject."

On Representation of Integers by Binary Quadratic Forms in Algebraic Number Fields

Author : Stig Christofferson
Publisher :
ISBN 13 :
Total Pages : 52 pages
Book Rating : 4.3/5 (243 download)

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Book Synopsis On Representation of Integers by Binary Quadratic Forms in Algebraic Number Fields by : Stig Christofferson

Download or read book On Representation of Integers by Binary Quadratic Forms in Algebraic Number Fields written by Stig Christofferson and published by . This book was released on 1962 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Binary Quadratic Forms

Author : Johannes Buchmann
Publisher : Springer Science & Business Media
ISBN 13 : 3540463682
Total Pages : 328 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Binary Quadratic Forms by : Johannes Buchmann

Download or read book Binary Quadratic Forms written by Johannes Buchmann and published by Springer Science & Business Media. This book was released on 2007-06-22 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with algorithmic problems related to binary quadratic forms. It uniquely focuses on the algorithmic aspects of the theory. The book introduces the reader to important areas of number theory such as diophantine equations, reduction theory of quadratic forms, geometry of numbers and algebraic number theory. The book explains applications to cryptography and requires only basic mathematical knowledge. The author is a world leader in number theory.

Quadratic Irrationals

Author : Franz Halter-Koch
Publisher : CRC Press
ISBN 13 : 1466591846
Total Pages : 431 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Quadratic Irrationals by : Franz Halter-Koch

Download or read book Quadratic Irrationals written by Franz Halter-Koch and published by CRC Press. This book was released on 2013-06-17 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quadratic Irrationals: An Introduction to Classical Number Theory gives a unified treatment of the classical theory of quadratic irrationals. Presenting the material in a modern and elementary algebraic setting, the author focuses on equivalence, continued fractions, quadratic characters, quadratic orders, binary quadratic forms, and class groups.T

Arithmetic of Quadratic Forms

Author : Yoshiyuki Kitaoka
Publisher : Cambridge University Press
ISBN 13 : 9780521649964
Total Pages : 292 pages
Book Rating : 4.6/5 (499 download)

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Book Synopsis Arithmetic of Quadratic Forms by : Yoshiyuki Kitaoka

Download or read book Arithmetic of Quadratic Forms written by Yoshiyuki Kitaoka and published by Cambridge University Press. This book was released on 1999-04-29 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an introduction to quadratic forms.

Introduction to Quadratic Forms over Fields

Author : T.Y. Lam
Publisher : American Mathematical Soc.
ISBN 13 : 9780821872413
Total Pages : 578 pages
Book Rating : 4.8/5 (724 download)

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Book Synopsis Introduction to Quadratic Forms over Fields by : T.Y. Lam

Download or read book Introduction to Quadratic Forms over Fields written by T.Y. Lam and published by American Mathematical Soc.. This book was released on with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new version of the author's prizewinning book, Algebraic Theory of Quadratic Forms (W. A. Benjamin, Inc., 1973), gives a modern and self-contained introduction to the theory of quadratic forms over fields of characteristic different from two. Starting with few prerequisites beyond linear algebra, the author charts an expert course from Witt's classical theory of quadratic forms, quaternion and Clifford algebras, Artin-Schreier theory of formally real fields, and structural theorems on Witt rings, to the theory of Pfister forms, function fields, and field invariants. These main developments are seamlessly interwoven with excursions into Brauer-Wall groups, local and global fields, trace forms, Galois theory, and elementary algebraic K-theory, to create a uniquely original treatment of quadratic form theory over fields. Two new chapters totaling more than 100 pages have been added to the earlier incarnation of this book to take into account some of the newer results and more recent viewpoints in the area. As is characteristic of this author's expository style, the presentation of the main material in this book is interspersed with a copious number of carefully chosen examples to illustrate the general theory. This feature, together with a rich stock of some 280 exercises for the thirteen chapters, greatly enhances the pedagogical value of this book, both as a graduate text and as a reference work for researchers in algebra, number theory, algebraic geometry, algebraic topology, and geometric topology.

Algebraic Number Fields

Author : Gerald J. Janusz
Publisher : American Mathematical Soc.
ISBN 13 : 0821804294
Total Pages : 288 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algebraic Number Fields by : Gerald J. Janusz

Download or read book Algebraic Number Fields written by Gerald J. Janusz and published by American Mathematical Soc.. This book was released on 1996 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.