Compositions Of Quadratic Forms

Author : Daniel B. Shapiro
Publisher : Walter de Gruyter
Page : 433 pages
File Size : 44,6 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783110824834

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Compositions of Quadratic Forms by Daniel B. Shapiro Pdf

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Author : J. W. S. Cassels
Publisher : Courier Dover Publications
Page : 429 pages
File Size : 55,9 Mb
Release : 2008-08-08
Category : Mathematics
ISBN : 9780486466705

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Rational Quadratic Forms by J. W. S. Cassels Pdf

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 : Duncan A. Buell
Publisher : Springer Science & Business Media
Page : 266 pages
File Size : 55,9 Mb
Release : 1989-08-25
Category : Mathematics
ISBN : 0387970371

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Binary Quadratic Forms by Duncan A. Buell Pdf

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 : Richard S. Elman,Nikita Karpenko,Alexander Merkurjev
Publisher : American Mathematical Soc.
Page : 456 pages
File Size : 50,7 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 : Anatoliĭ Nikolaevich Andrianov
Publisher : [Kingston, Ont.] : Queen's University
Page : 72 pages
File Size : 48,6 Mb
Release : 1992
Category : Mathematics
ISBN : OSU:32435026349878

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Queen's Lectures on Arithmetical Composition of Quadratic Forms by Anatoliĭ Nikolaevich Andrianov Pdf

Author : John Voight
Publisher : Springer Nature
Page : 877 pages
File Size : 52,5 Mb
Release : 2021-06-28
Category : Mathematics
ISBN : 9783030566944

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Quaternion Algebras by John Voight Pdf

This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.

Author : Burton W Jones
Publisher : American Mathematical Soc.
Page : 212 pages
File Size : 55,8 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 : John Horton Conway,Francis Y. C. Fung
Publisher : Cambridge University Press
Page : 180 pages
File Size : 42,5 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 : Irving Kaplansky
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 48,5 Mb
Release : 1995-04-13
Category : Mathematics
ISBN : 0387944060

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Selected Papers and Other Writings by Irving Kaplansky Pdf

It is not often that one gets to write a preface to a collection of one's own papers. The most urgent task is to thank the people who made this book possible. That means first of all Hy Bass who, on behalf of Springer-Verlag, approached me about the idea. The late Walter Kaufmann-Biihler was very encouraging; Paulo Ribenboim helped in an important way; and Ina Lindemann saw the project through with tact and skill that I deeply appreciate. My wishes have been indulged in two ways. First, I was allowed to follow up each selected paper with an afterthought. Back in my student days I became aware of the Gesammelte Mathematische Werke of Dedekind, edited by Fricke, Noether, and Ore. I was impressed by the editors' notes that followed most of the papers and found them very usefuL A more direct model was furnished by the collected papers of Lars Ahlfors, in which the author himself supplied afterthoughts for each paper or group of papers. These were tough acts to follow, but I hope that some readers will find at least some of my afterthoughts interesting. Second, I was permitted to add eight previously unpublished items. My model here, to a certain extent, was the charming little book, A Mathematician's Miscel lany by J. E. Littlewood. In picking these eight I had quite a selection to make -from fourteen loose-leaf notebooks of such writings. Here again I hope that at least some will be found to be of interest.

Author : David A. Cox
Publisher : John Wiley & Sons
Page : 372 pages
File Size : 55,7 Mb
Release : 2011-10-24
Category : Mathematics
ISBN : 9781118031001

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Primes of the Form x2 + ny2 by David A. Cox Pdf

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 : Nikolaĭ Vladimirovich Efimov
Publisher : Unknown
Page : 184 pages
File Size : 52,6 Mb
Release : 1964
Category : Forms, Quadratic
ISBN : STANFORD:36105030080209

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Quadratic Forms and Matrices by Nikolaĭ Vladimirovich Efimov Pdf

Author : Ricardo Baeza
Publisher : American Mathematical Soc.
Page : 424 pages
File Size : 47,9 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 : 48,5 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 : Eva Bayer-Fluckiger,Conference on Quadratic Forms and Their Applications,David Lewis,Andrew Ranicki,Conference on Quadratic Forms and Their Applications Staff
Publisher : American Mathematical Soc.
Page : 311 pages
File Size : 50,9 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821827796

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Quadratic Forms and Their Applications by Eva Bayer-Fluckiger,Conference on Quadratic Forms and Their Applications,David Lewis,Andrew Ranicki,Conference on Quadratic Forms and Their Applications Staff Pdf

This volume outlines the proceedings of the conference on 'Quadratic Forms and Their Applications' held at University College Dublin. It includes survey articles and research papers ranging from applications in topology and geometry to the algebraic theory of quadratic forms and its history. Various aspects of the use of quadratic forms in algebra, analysis, topology, geometry, and number theory are addressed. Special features include the first published proof of the Conway-Schneeberger Fifteen Theorem on integer-valued quadratic forms and the first English-language biography of Ernst Witt, founder of the theory of quadratic forms.

Author : O. Taussky
Publisher : CRC Press
Page : 152 pages
File Size : 41,9 Mb
Release : 2020-12-17
Category : Mathematics
ISBN : 9781000116809

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Ternary Quadratic Forms and Norms by O. Taussky Pdf

This book covers topics including the Redei-Reichardt theorem, automorphs of ternary quadratic forms, facts concerning rational matrices leading to integral ternary forms representing zero, characteristics polynomials of symmetric matrices, and Gauss' theory of ternary quadratic forms.