The Arithmetic Theory Of Quadratic Forms
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Author | : Burton W Jones |
Publisher | : American Mathematical Soc. |
Total Pages | : 212 |
Release | : 1950-12-31 |
Genre | : Forms, Binary |
ISBN | : 1614440107 |
This monograph presents the central ideas of the arithmetic theory of quadratic forms in self-contained form, assuming only knowledge of the fundamentals of matric theory and the theory of numbers. Pertinent concepts of p -adic numbers and quadratic ideals are introduced. It would have been possible to avoid these concepts, but the theory gains elegance as well as breadth by the introduction of such relationships. Some results, and many of the methods, are here presented for the first time. The development begins with the classical theory in the field of reals from the point of view of representation theory; for in these terms, many of the later objectives and methods may be revealed. The successive chapters gradually narrow the fields and rings until one has the tools at hand to deal with the classical problems in the ring of rational integers. The analytic theory of quadratic forms is not dealt with because of the delicate analysis involved. However, some of the more important results are stated and references are given.
Author | : Onorato Timothy O’Meara |
Publisher | : Springer |
Total Pages | : 354 |
Release | : 2013-12-01 |
Genre | : Mathematics |
ISBN | : 366241922X |
Author | : Larry J. Gerstein |
Publisher | : American Mathematical Soc. |
Total Pages | : 274 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 0821844652 |
The arithmetic theory of quadratic forms is a rich branch of number theory that has had important applications to several areas of pure mathematics--particularly group theory and topology--as well as to cryptography and coding theory. This book is a self-contained introduction to quadratic forms that is based on graduate courses the author has taught many times. It leads the reader from foundation material up to topics of current research interest--with special attention to the theory over the integers and over polynomial rings in one variable over a field--and requires only a basic background in linear and abstract algebra as a prerequisite. Whenever possible, concrete constructions are chosen over more abstract arguments. The book includes many exercises and explicit examples, and it is appropriate as a textbook for graduate courses or for independent study. To facilitate further study, a guide to the extensive literature on quadratic forms is provided.
Author | : Burton Wadsworth Jones |
Publisher | : MAA Press |
Total Pages | : 232 |
Release | : 1950 |
Genre | : Mathematics |
ISBN | : |
Author | : Goro Shimura |
Publisher | : Springer Science & Business Media |
Total Pages | : 245 |
Release | : 2010-08-09 |
Genre | : Mathematics |
ISBN | : 1441917322 |
This book is divided into two parts. The first part is preliminary and consists of algebraic number theory and the theory of semisimple algebras. There are two principal topics: classification of quadratic forms and quadratic Diophantine equations. The second topic is a new framework which contains the investigation of Gauss on the sums of three squares as a special case. To make the book concise, the author proves some basic theorems in number theory only in some special cases. However, the book is self-contained when the base field is the rational number field, and the main theorems are stated with an arbitrary number field as the base field. So the reader familiar with class field theory will be able to learn the arithmetic theory of quadratic forms with no further references.
Author | : Yoshiyuki Kitaoka |
Publisher | : Cambridge University Press |
Total Pages | : 292 |
Release | : 1999-04-29 |
Genre | : Mathematics |
ISBN | : 9780521649964 |
Provides an introduction to quadratic forms.
Author | : Ricardo Baeza |
Publisher | : American Mathematical Soc. |
Total Pages | : 424 |
Release | : 2009-08-14 |
Genre | : Mathematics |
ISBN | : 0821846485 |
This volume presents a collection of articles that are based on talks delivered at the International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms held in Frutillar, Chile in December 2007. The theory of quadratic forms is closely connected with a broad spectrum of areas in algebra and number theory. The articles in this volume deal mainly with questions from the algebraic, geometric, arithmetic, and analytic theory of quadratic forms, and related questions in algebraic group theory and algebraic geometry.
Author | : Jones |
Publisher | : |
Total Pages | : 212 |
Release | : 1950-01-01 |
Genre | : |
ISBN | : 9780471447481 |
Author | : Ricardo Baeza |
Publisher | : American Mathematical Soc. |
Total Pages | : 364 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 082183441X |
This proceedings volume contains papers presented at the International Conference on the algebraic and arithmetic theory of quadratic forms held in Talca (Chile). The modern theory of quadratic forms has connections with a broad spectrum of mathematical areas including number theory, geometry, and K-theory. This volume contains survey and research articles covering the range of connections among these topics. The survey articles bring readers up-to-date on research and open problems in representation theory of integral quadratic forms, the algebraic theory of finite square class fields, and developments in the theory of Witt groups of triangulated categories. The specialized articles present important developments in both the algebraic and arithmetic theory of quadratic forms, as well as connections to geometry and K-theory. The volume is suitable for graduate students and research mathematicians interested in various aspects of the theory of quadratic forms.
Author | : O. Timothy O'Meara |
Publisher | : Springer Science & Business Media |
Total Pages | : 356 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642620310 |
From the reviews: "Anyone who has heard O'Meara lecture will recognize in every page of this book the crispness and lucidity of the author's style. [...] The organization and selection of material is superb. [...] deserves high praise as an excellent example of that too-rare type of mathematical exposition combining conciseness with clarity." Bulletin of the AMS