Quadratic Forms -- Algebra, Arithmetic, and Geometry

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Publisher : American Mathematical Soc.
ISBN 13 : 0821846485
Total Pages : 424 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Quadratic Forms -- Algebra, Arithmetic, and Geometry by : Ricardo Baeza

Download or read book Quadratic Forms -- Algebra, Arithmetic, and Geometry written by Ricardo Baeza and published by American Mathematical Soc.. This book was released on 2009-08-14 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Arithmetic of Quadratic Forms

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Publisher : Springer Science & Business Media
ISBN 13 : 1441917322
Total Pages : 245 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Arithmetic of Quadratic Forms by : Goro Shimura

Download or read book Arithmetic of Quadratic Forms written by Goro Shimura and published by Springer Science & Business Media. This book was released on 2010-08-09 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Sensual (quadratic) Form

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Publisher : American Mathematical Soc.
ISBN 13 : 1470448424
Total Pages : 152 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Sensual (quadratic) Form by : John Horton Conway

Download or read book The Sensual (quadratic) Form written by John Horton Conway and published by American Mathematical Soc.. This book was released on 1997-12-31 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: John Horton Conway's unique approach to quadratic forms was the subject of the Hedrick Lectures that he gave in August of 1991 at the Joint Meetings of the Mathematical Association of America and the American Mathematical Society in Orono, Maine. This book presents the substance of those lectures. The book should not be thought of as a serious textbook on the theory of quadratic forms. It consists rather of a number of essays on particular aspects of quadratic forms that have interested the author. The lectures are self-contained and will be accessible to the generally informed reader who has no particular background in quadratic form theory. The minor exceptions should not interrupt the flow of ideas. The afterthoughts to the lectures contain discussion of related matters that occasionally presuppose greater knowledge.

Recent Advances in Real Algebraic Geometry and Quadratic Forms

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821854891
Total Pages : 420 pages
Book Rating : 4.8/5 (548 download)

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Book Synopsis Recent Advances in Real Algebraic Geometry and Quadratic Forms by : Bill Jacob

Download or read book Recent Advances in Real Algebraic Geometry and Quadratic Forms written by Bill Jacob and published by American Mathematical Soc.. This book was released on 1994 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers collected here present an up-to-date record of the current research developments in the fields of real algebraic geometry and quadratic forms. Articles range from the technical to the expository and there are also indications to new research directions.

Quadratic Forms with Applications to Algebraic Geometry and Topology

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Publisher : Cambridge University Press
ISBN 13 : 0521467551
Total Pages : 191 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Quadratic Forms with Applications to Algebraic Geometry and Topology by : Albrecht Pfister

Download or read book Quadratic Forms with Applications to Algebraic Geometry and Topology written by Albrecht Pfister and published by Cambridge University Press. This book was released on 1995-09-28 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: A gem of a book bringing together 30 years worth of results that are certain to interest anyone whose research touches on quadratic forms.

The Algebraic and Geometric Theory of Quadratic Forms

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821873229
Total Pages : 456 pages
Book Rating : 4.8/5 (732 download)

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Book Synopsis The Algebraic and Geometric Theory of Quadratic Forms by : Richard S. Elman

Download or read book The Algebraic and Geometric Theory of Quadratic Forms written by Richard S. Elman and published by American Mathematical Soc.. This book was released on 2008-07-15 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive study of the algebraic theory of quadratic forms, from classical theory to recent developments, including results and proofs that have never been published. The book is written from the viewpoint of algebraic geometry and includes the theory of quadratic forms over fields of characteristic two, with proofs that are characteristic independent whenever possible. For some results both classical and geometric proofs are given. Part I includes classical algebraic theory of quadratic and bilinear forms and answers many questions that have been raised in the early stages of the development of the theory. Assuming only a basic course in algebraic geometry, Part II presents the necessary additional topics from algebraic geometry including the theory of Chow groups, Chow motives, and Steenrod operations. These topics are used in Part III to develop a modern geometric theory of quadratic forms.

Quadratic Forms, Linear Algebraic Groups, and Cohomology

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Publisher : Springer Science & Business Media
ISBN 13 : 1441962115
Total Pages : 344 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Quadratic Forms, Linear Algebraic Groups, and Cohomology by : Skip Garibaldi

Download or read book Quadratic Forms, Linear Algebraic Groups, and Cohomology written by Skip Garibaldi and published by Springer Science & Business Media. This book was released on 2010-07-16 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developments in Mathematics is a book series devoted to all areas of mathematics, pure and applied. The series emphasizes research monographs describing the latest advances. Edited volumes that focus on areas that have seen dramatic progress, or are of special interest, are encouraged as well.

The Sensual (Quadratic) Form

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Author :
Publisher : Cambridge University Press
ISBN 13 : 9780883850305
Total Pages : 180 pages
Book Rating : 4.8/5 (53 download)

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Book Synopsis The Sensual (Quadratic) Form by : John Horton Conway

Download or read book The Sensual (Quadratic) Form written by John Horton Conway and published by Cambridge University Press. This book was released on 1997 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quadratic forms are presented in a pictorial way, elucidating many topics in algebra, number theory and geometry.

The Arithmetic Theory of Quadratic Forms

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Publisher : American Mathematical Soc.
ISBN 13 : 1614440107
Total Pages : 212 pages
Book Rating : 4.6/5 (144 download)

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Book Synopsis The Arithmetic Theory of Quadratic Forms by : Burton W Jones

Download or read book The Arithmetic Theory of Quadratic Forms written by Burton W Jones and published by American Mathematical Soc.. This book was released on 1950-12-31 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic and Arithmetic Theory of Quadratic Forms

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Publisher : American Mathematical Soc.
ISBN 13 : 082183441X
Total Pages : 350 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algebraic and Arithmetic Theory of Quadratic Forms by : International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms (2002

Download or read book Algebraic and Arithmetic Theory of Quadratic Forms written by International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms (2002 and published by American Mathematical Soc.. This book was released on 2004 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Geometry of Positive Quadratic Forms

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821830703
Total Pages : 268 pages
Book Rating : 4.8/5 (37 download)

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Book Synopsis The Geometry of Positive Quadratic Forms by : Sergeĭ Sergeevich Ryshkov

Download or read book The Geometry of Positive Quadratic Forms written by Sergeĭ Sergeevich Ryshkov and published by American Mathematical Soc.. This book was released on 1983 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers and articles about quadratic forms.

Quaternion Orders, Quadratic Forms, and Shimura Curves

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821833599
Total Pages : 232 pages
Book Rating : 4.8/5 (335 download)

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Book Synopsis Quaternion Orders, Quadratic Forms, and Shimura Curves by : Montserrat Alsina

Download or read book Quaternion Orders, Quadratic Forms, and Shimura Curves written by Montserrat Alsina and published by American Mathematical Soc.. This book was released on 2004 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shimura curves are a far-reaching generalization of the classical modular curves. They lie at the crossroads of many areas, including complex analysis, hyperbolic geometry, algebraic geometry, algebra, and arithmetic. This monograph presents Shimura curves from a theoretical and algorithmic perspective. The main topics are Shimura curves defined over the rational number field, the construction of their fundamental domains, and the determination of their complex multiplicationpoints. The study of complex multiplication points in Shimura curves leads to the study of families of binary quadratic forms with algebraic coefficients and to their classification by arithmetic Fuchsian groups. In this regard, the authors develop a theory full of new possibilities that parallels Gauss'theory on the classification of binary quadratic forms with integral coefficients by the action of the modular group. This is one of the few available books explaining the theory of Shimura curves at the graduate student level. Each topic covered in the book begins with a theoretical discussion followed by carefully worked-out examples, preparing the way for further research.

Algebraic and Arithmetic Theory of Quadratic Forms

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 9780821856796
Total Pages : 350 pages
Book Rating : 4.8/5 (567 download)

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Book Synopsis Algebraic and Arithmetic Theory of Quadratic Forms by :

Download or read book Algebraic and Arithmetic Theory of Quadratic Forms written by and published by American Mathematical Soc.. This book was released on 2004 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Variations on a Theme of Euler

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Publisher : Springer Science & Business Media
ISBN 13 : 1475723261
Total Pages : 356 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Variations on a Theme of Euler by : Takashi Ono

Download or read book Variations on a Theme of Euler written by Takashi Ono and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first six chapters and Appendix 1 of this book appeared in Japanese in a book of the same title 15years aga (Jikkyo, Tokyo, 1980).At the request of some people who do not wish to learn Japanese, I decided to rewrite my old work in English. This time, I added a chapter on the arithmetic of quadratic maps (Chapter 7) and Appendix 2, A Short Survey of Subsequent Research on Congruent Numbers, by M. Kida. Some 20 years ago, while rifling through the pages of Selecta Heinz Hopj (Springer, 1964), I noticed a system of three quadratic forms in four variables with coefficientsin Z that yields the map of the 3-sphere to the 2-sphere with the Hopf invariant r =1 (cf. Selecta, p. 52). Immediately I feit that one aspect of classical and modern number theory, including quadratic forms (Pythagoras, Fermat, Euler, and Gauss) and space elliptic curves as intersection of quadratic surfaces (Fibonacci, Fermat, and Euler), could be considered as the number theory of quadratic maps-especially of those maps sending the n-sphere to the m-sphere, i.e., the generalized Hopf maps. Having these in mind, I deliveredseverallectures at The Johns Hopkins University (Topics in Number Theory, 1973-1974, 1975-1976, 1978-1979, and 1979-1980). These lectures necessarily contained the following three basic areas of mathematics: v vi Preface Theta Simple Functions Aigebras Elliptic Curves Number Theory Figure P.l.

Quadratic and Hermitian Forms

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821860083
Total Pages : 362 pages
Book Rating : 4.8/5 (6 download)

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Book Synopsis Quadratic and Hermitian Forms by : McMaster University

Download or read book Quadratic and Hermitian Forms written by McMaster University and published by American Mathematical Soc.. This book was released on 1984 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the 1983 Seminar on Quadratic and Hermitian Forms held at McMaster University, July 1983. Between 1945 and 1965, most of the work in quadratic (and hermitian) forms took place in arithmetic theory (M Eichler, M Kneser, O T O'Meara).

Integral Quadratic Forms and Lattices

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Publisher : American Mathematical Soc.
ISBN 13 : 0821819496
Total Pages : 314 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Integral Quadratic Forms and Lattices by : International Conference on Integral Quadratic Forms and Lattices

Download or read book Integral Quadratic Forms and Lattices written by International Conference on Integral Quadratic Forms and Lattices and published by American Mathematical Soc.. This book was released on 1999 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of an international conference held at Seoul National University (Korea). Talks covered recent developments in diverse areas related to the theory of integral quadratic forms and hermitian forms, local densities, linear relations and congruences of theta series, zeta functions of prehomogeneous vector spaces, lattices with maximal finite matrix groups, globally irreducible lattices, Mordell-Weil lattices, and more. Articles in the volume represent expository lectures by leading experts on recent developments in the field. The book offers a comprehensive introduction to the current state of knowledge in the arithmetic theory of quadratic forms and provides active directions of research with new results. Topics addressed in the volume emphasize connections with related fields, such as group theory, arithmetic geometry, analytic number theory, and modular forms. The book is an excellent introductory guide for students as well as a rich reference source for researchers.

Geometric Methods in the Algebraic Theory of Quadratic Forms

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Publisher : Springer Science & Business Media
ISBN 13 : 9783540207283
Total Pages : 212 pages
Book Rating : 4.2/5 (72 download)

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Book Synopsis Geometric Methods in the Algebraic Theory of Quadratic Forms by :

Download or read book Geometric Methods in the Algebraic Theory of Quadratic Forms written by and published by Springer Science & Business Media. This book was released on 2004 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: