Quadratic Forms Algebra Arithmetic And Geometry

Author : Ricardo Baeza
Publisher : American Mathematical Soc.
Page : 424 pages
File Size : 52,5 Mb
Release : 2009-08-14
Category : Mathematics
ISBN : 9780821846483

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Quadratic Forms -- Algebra, Arithmetic, and Geometry by Ricardo Baeza Pdf

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 : John Horton Conway
Publisher : American Mathematical Soc.
Page : 152 pages
File Size : 40,6 Mb
Release : 1997-12-31
Category : Electronic
ISBN : 9781470448424

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The Sensual (quadratic) Form by John Horton Conway Pdf

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.

Author : International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms (2002,International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms (2002 : Universidad de Talca)
Publisher : American Mathematical Soc.
Page : 350 pages
File Size : 44,6 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821834411

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Algebraic and Arithmetic Theory of Quadratic Forms by International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms (2002,International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms (2002 : Universidad de Talca) Pdf

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.

Author : Skip Garibaldi,R. Sujatha,Venapally Suresh
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 51,8 Mb
Release : 2010-07-16
Category : Mathematics
ISBN : 9781441962119

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Quadratic Forms, Linear Algebraic Groups, and Cohomology by Skip Garibaldi,R. Sujatha,Venapally Suresh Pdf

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.

Author : Montserrat Alsina,Pilar Bayer i Isant
Publisher : American Mathematical Soc.
Page : 232 pages
File Size : 46,5 Mb
Release : 2004
Category : Mathematics
ISBN : 0821833596

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Quaternion Orders, Quadratic Forms, and Shimura Curves by Montserrat Alsina,Pilar Bayer i Isant Pdf

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.

Author : Anonim
Publisher : American Mathematical Soc.
Page : 350 pages
File Size : 51,7 Mb
Release : 2004
Category : Forms, Quadratic
ISBN : 0821856790

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Algebraic and Arithmetic Theory of Quadratic Forms by Anonim Pdf

Author : John Horton Conway,Francis Y. C. Fung
Publisher : Cambridge University Press
Page : 180 pages
File Size : 43,5 Mb
Release : 1997
Category : Mathematics
ISBN : 0883850303

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The Sensual (Quadratic) Form by John Horton Conway,Francis Y. C. Fung Pdf

Quadratic forms are presented in a pictorial way, elucidating many topics in algebra, number theory and geometry.

Author : Burton W Jones
Publisher : American Mathematical Soc.
Page : 212 pages
File Size : 51,5 Mb
Release : 1950-12-31
Category : Forms, Binary
ISBN : 9781614440109

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The Arithmetic Theory of Quadratic Forms by Burton W Jones Pdf

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 : Bill Jacob,Tsit-Yuen Lam,Robert O. Robson
Publisher : American Mathematical Soc.
Page : 420 pages
File Size : 54,9 Mb
Release : 1994
Category : Mathematics
ISBN : 0821854895

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Recent Advances in Real Algebraic Geometry and Quadratic Forms by Bill Jacob,Tsit-Yuen Lam,Robert O. Robson Pdf

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.

Author : Takashi Ono
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 54,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475723267

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Variations on a Theme of Euler by Takashi Ono Pdf

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.

Author : Richard S. Elman,Nikita Karpenko,Alexander Merkurjev
Publisher : American Mathematical Soc.
Page : 456 pages
File Size : 53,8 Mb
Release : 2008-07-15
Category : Mathematics
ISBN : 0821873229

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The Algebraic and Geometric Theory of Quadratic Forms by Richard S. Elman,Nikita Karpenko,Alexander Merkurjev Pdf

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.

Author : Albrecht Pfister
Publisher : Cambridge University Press
Page : 191 pages
File Size : 44,8 Mb
Release : 1995-09-28
Category : Mathematics
ISBN : 9780521467551

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Quadratic Forms with Applications to Algebraic Geometry and Topology by Albrecht Pfister Pdf

A gem of a book bringing together 30 years worth of results that are certain to interest anyone whose research touches on quadratic forms.

Author : International Conference on Integral Quadratic Forms and Lattices
Publisher : American Mathematical Soc.
Page : 314 pages
File Size : 46,6 Mb
Release : 1999
Category : Forms, Quadratic
ISBN : 9780821819494

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Integral Quadratic Forms and Lattices by International Conference on Integral Quadratic Forms and Lattices Pdf

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.

Author : Onorato Timothy O’Meara
Publisher : Springer
Page : 354 pages
File Size : 42,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783662419229

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Introduction to Quadratic Forms by Onorato Timothy O’Meara Pdf

Author : Montserrat Alsina and Pilar Bayer
Publisher : American Mathematical Soc.
Page : 216 pages
File Size : 40,7 Mb
Release : 2024-06-17
Category : Electronic
ISBN : 9780821869833

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Quaternion Orders, Quadratic Forms, and Shimura Curves by Montserrat Alsina and Pilar Bayer Pdf

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 multiplication points. 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. Titles in this series are co-published with the Centre de Recherches Mathématiques.