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Author : George Hoffman Cresse
Publisher :
ISBN 13 :
Total Pages : 117 pages
Book Rating : 4.01/5 ( download)
Download or read book The Class Number of Binary Quadratic Forms ... written by George Hoffman Cresse and published by . This book was released on 1923 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : George Hoffman Cresse
Publisher :
ISBN 13 :
Total Pages : 105 pages
Book Rating : 4.69/5 ( download)
Download or read book The Class Number of Binary Quadratic Forms written by George Hoffman Cresse and published by . This book was released on 1923 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Duncan A. Buell
Publisher : Springer Science & Business Media
ISBN 13 : 1461245427
Total Pages : 249 pages
Book Rating : 4.21/5 ( download)
Download or read book Binary Quadratic Forms written by Duncan A. Buell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first coherent exposition of the theory of binary quadratic forms was given by Gauss in the Disqnisitiones Arithmeticae. During the nine teenth century, as the theory of ideals and the rudiments of algebraic number theory were developed, it became clear that this theory of bi nary quadratic forms, so elementary and computationally explicit, was indeed just a special case of a much more elega,nt and abstract theory which, unfortunately, is not computationally explicit. In recent years the original theory has been laid aside. Gauss's proofs, which involved brute force computations that can be done in what is essentially a two dimensional vector space, have been dropped in favor of n-dimensional arguments which prove the general theorems of algebraic number the ory. In consequence, this elegant, yet pleasantly simple, theory has been neglected even as some of its results have become extremely useful in certain computations. I find this neglect unfortunate, because binary quadratic forms have two distinct attractions. First, the subject involves explicit computa tion and many of the computer programs can be quite simple. The use of computers in experimenting with examples is both meaningful and enjoyable; one can actually discover interesting results by com puting examples, noticing patterns in the "data," and then proving that the patterns result from the conclusion of some provable theorem.
Author : George Hoffman Cresse
Publisher :
ISBN 13 : 9781418163419
Total Pages : pages
Book Rating : 4.14/5 ( download)
Download or read book The Class Number of Binary Quadratic Forms ... by George Hoffman Cresse written by George Hoffman Cresse and published by . This book was released on 2004-01-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Johannes Buchmann
Publisher : Springer Science & Business Media
ISBN 13 : 3540463682
Total Pages : 328 pages
Book Rating : 4.89/5 ( download)
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.
Author : J. W. S. Cassels
Publisher : Courier Dover Publications
ISBN 13 : 0486466701
Total Pages : 429 pages
Book Rating : 4.05/5 ( download)
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.
Author : Franz Halter-Koch
Publisher : CRC Press
ISBN 13 : 1466591846
Total Pages : 431 pages
Book Rating : 4.44/5 ( download)
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
Author : David A. Cox
Publisher : John Wiley & Sons
ISBN 13 : 1118031008
Total Pages : 372 pages
Book Rating : 4.01/5 ( download)
Download or read book Primes of the Form x2 + ny2 written by David A. Cox and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern number theory began with the work of Euler and Gauss to understand and extend the many unsolved questions left behind by Fermat. In the course of their investigations, they uncovered new phenomena in need of explanation, which over time led to the discovery of field theory and its intimate connection with complex multiplication. While most texts concentrate on only the elementary or advanced aspects of this story, Primes of the Form x2 + ny2 begins with Fermat and explains how his work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. Further, the book shows how the results of Euler and Gauss can be fully understood only in the context of class field theory. Finally, in order to bring class field theory down to earth, the book explores some of the magnificent formulas of complex multiplication. The central theme of the book is the story of which primes p can be expressed in the form x2 + ny2. An incomplete answer is given using quadratic forms. A better though abstract answer comes from class field theory, and finally, a concrete answer is provided by complex multiplication. Along the way, the reader is introduced to some wonderful number theory. Numerous exercises and examples are included. The book is written to be enjoyed by readers with modest mathematical backgrounds. Chapter 1 uses basic number theory and abstract algebra, while chapters 2 and 3 require Galois theory and complex analysis, respectively.
Author : George Hoffmann Cresse
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.96/5 ( download)
Download or read book The Class Number of Binary Quadratic Forms, a Dissertation... by George Hoffmann Cresse written by George Hoffmann Cresse and published by . This book was released on 1923 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jeffrey Stopple
Publisher : Cambridge University Press
ISBN 13 : 9780521012539
Total Pages : 404 pages
Book Rating : 4.38/5 ( download)
Download or read book A Primer of Analytic Number Theory written by Jeffrey Stopple and published by Cambridge University Press. This book was released on 2003-06-23 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: An undergraduate-level 2003 introduction whose only prerequisite is a standard calculus course.
