Quaternary Quadratic Forms
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Quaternary Quadratic Forms
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Author : Gordon L. Nipp
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Quaternary Quadratic Forms written by Gordon L. Nipp and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book of tables includes a reduced representative of each class of. integral positive definite primitive quaternary quadratic forms through discriminant 1732. The classes are grouped into genera; also included are Hasse symbols, the number of automorphs and the level of each such form, and the mass of each genus. An appendix lists p-adic densities and p-adic Jordan splittings for each genus in the tables for p = 2 and for each odd prime p dividing the discriminant. The book is divided into several sections. The first, an introductory section, contains background material, an explanation of the techniques used to generate the information contained in the tables, a description of the format of the tables, some instructions for computer use, examples, and references. The next section contains a printed version of the tables through discriminant 500, included to allow the reader to peruse at least this much without the inconvenience of making his/her own hard copy via the computer. Because of their special interest, we include tables of discriminants 729 and 1729 at the end of this section. Limitations of space preclude publication of more than this in printed form. A printed appendix through discriminant 500 and for discriminants 729 and 1729 follows. The complete tables and appendix through discriminant 1732 are compressed onto the accompanying 3.5 inch disk, formatted for use in a PC-compatible computer and ready for research use particularly when uploaded to a mainframe. Documentation is included in the Introduction.
Reduced Positive Quaternary Quadratic Forms
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Author : Stanmore Brooks Townes
language : en
Publisher:
Release Date : 1936
Reduced Positive Quaternary Quadratic Forms written by Stanmore Brooks Townes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1936 with Forms, Quadratic categories.
The Minima Of Indefinite Quaternary Quadratic Forms
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Author : Alexander Oppenheim
language : en
Publisher:
Release Date : 1931
The Minima Of Indefinite Quaternary Quadratic Forms written by Alexander Oppenheim and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1931 with Forms, Quadratic categories.
Studies In The Theory Of Numbers
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Author : Leonard Eugene Dickson
language : en
Publisher: Chelsea Publishing Company, Incorporated
Release Date : 1957
Studies In The Theory Of Numbers written by Leonard Eugene Dickson and has been published by Chelsea Publishing Company, Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 1957 with Forms, Quadratic categories.
Pt. I. Arithmetic of ternary quadratic forms. Quadratic forms in n variables -- Introduction to ternary quadratic forms; universal forms -- Representation of binary forms by ternary forms -- Equivalence of indefinite, ternary, quadratic forms -- Genera and representation of numbers -- Quadratic Diophantine equations -- pt. II. Minima of indefinite quadratic forms. Minima of indefinite, binary quadratic forms -- Minima of indefinite, ternary, quadratic forms -- Minima of indefinite, quaternary, quadratic forms -- Tabulation of reduced, integral, ternary, quadratic forms which are indefinite, but not zero forms -- pt. III. Miscellaneous investigations of quadratic forms. Reduced, positive, quadratic forms; their minima -- Universal, zero, quadratic forms -- Number of representations as a sum of 5, 6, 7, or 8 squares.
Rational Quadratic Forms
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Author : J. W. S. Cassels
language : en
Publisher: Courier Dover Publications
Release Date : 2008-08-08
Rational Quadratic Forms written by J. W. S. Cassels and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-08 with Mathematics categories.
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.
History Of The Theory Of Numbers Volume Iii
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Author : Leonard Eugene Dickson
language : en
Publisher: Courier Corporation
Release Date : 2005-06-03
History Of The Theory Of Numbers Volume Iii written by Leonard Eugene Dickson and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-03 with Mathematics categories.
The three-volume series History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This final volume in the series, which is suitable for upper-level undergraduates and graduate students, is devoted to quadratic and higher forms. It can be read independently of the preceding volumes, which explore divisibility and primality and diophantine analysis. Topics include reduction and equivalence of binary quadratic forms and representation of integers; composition of binary quadratic forms; the composition of orders and genera; irregular determinants; classes of binary quadratic forms with integral coefficients; binary quadratic forms whose coefficients are complete integers or integers of a field; classes of binary quadratic forms with complex integral coefficients; ternary and quaternary quadratic forms; cubic forms in three or more variables; binary hermitian forms; bilinear forms, matrices, and linear substitutions; congruencial theory of forms; and many other related topics. Indexes of authors cited and subjects appear at the end of the book.
Ternary Quadratic Forms And Norms
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Author : O. Taussky
language : en
Publisher: CRC Press
Release Date : 2020-12-17
Ternary Quadratic Forms And Norms written by O. Taussky and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-17 with Mathematics categories.
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.
Quaternion Algebras
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Author : John Voight
language : en
Publisher: Springer Nature
Release Date : 2021-06-28
Quaternion Algebras written by John Voight and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-28 with Mathematics categories.
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.
Algebraic And Arithmetic Theory Of Quadratic Forms
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Author : Ricardo Baeza
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Algebraic And Arithmetic Theory Of Quadratic Forms written by Ricardo Baeza and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
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.
Quadratic And Higher Degree Forms
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Author : Krishnaswami Alladi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-13
Quadratic And Higher Degree Forms written by Krishnaswami Alladi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-13 with Mathematics categories.
In the last decade, the areas of quadratic and higher degree forms have witnessed dramatic advances. This volume is an outgrowth of three seminal conferences on these topics held in 2009, two at the University of Florida and one at the Arizona Winter School. The volume also includes papers from the two focused weeks on quadratic forms and integral lattices at the University of Florida in 2010.Topics discussed include the links between quadratic forms and automorphic forms, representation of integers and forms by quadratic forms, connections between quadratic forms and lattices, and algorithms for quaternion algebras and quadratic forms. The book will be of interest to graduate students and mathematicians wishing to study quadratic and higher degree forms, as well as to established researchers in these areas. Quadratic and Higher Degree Forms contains research and semi-expository papers that stem from the presentations at conferences at the University of Florida as well as survey lectures on quadratic forms based on the instructional workshop for graduate students held at the Arizona Winter School. The survey papers in the volume provide an excellent introduction to various aspects of the theory of quadratic forms starting from the basic concepts and provide a glimpse of some of the exciting questions currently being investigated. The research and expository papers present the latest advances on quadratic and higher degree forms and their connections with various branches of mathematics.