Author: National Research Council (U.S.). Committee on tables of positive ternary quadratic formsPublisher:
ISBN:
Category : Forms, Quadratic
Languages : en
Pages : 58
Book Description
A Table of Eisenstein-reduced Positive Ternary Quadratic Forms of Determinant
Author: National Research Council (U.S.). Committee on tables of positive ternary quadratic formsPublisher:
ISBN:
Category : Forms, Quadratic
Languages : en
Pages : 58
Book Description
A Table of Eisenstein Reduced Positive Ternary Quadratic Forms of Determinant 'ɤ 200
Author: Quaternary Quadratic Forms
Author: Gordon L. NippPublisher: Springer Science & Business Media
ISBN: 1461231809
Category : Mathematics
Languages : en
Pages : 160
Book Description
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.
Rational Quadratic Forms
Author: J. W. S. CasselsPublisher: Courier Dover Publications
ISBN: 0486466701
Category : Mathematics
Languages : en
Pages : 429
Book Description
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.
The Arithmetic Theory of Quadratic Forms
Author: Burton W JonesPublisher: American Mathematical Soc.
ISBN: 1614440107
Category : Forms, Binary
Languages : en
Pages : 212
Book Description
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.
Report of the National Academy of Sciences
Author: National Academy of Sciences (U.S.)Publisher: National Academies
ISBN:
Category : Science
Languages : en
Pages : 810
Book Description
Sphere Packings, Lattices and Groups
Author: John H. ConwayPublisher: Springer Science & Business Media
ISBN: 1475720165
Category : Mathematics
Languages : en
Pages : 690
Book Description
The main themes. This book is mainly concerned with the problem of packing spheres in Euclidean space of dimensions 1,2,3,4,5, . . . . Given a large number of equal spheres, what is the most efficient (or densest) way to pack them together? We also study several closely related problems: the kissing number problem, which asks how many spheres can be arranged so that they all touch one central sphere of the same size; the covering problem, which asks for the least dense way to cover n-dimensional space with equal overlapping spheres; and the quantizing problem, important for applications to analog-to-digital conversion (or data compression), which asks how to place points in space so that the average second moment of their Voronoi cells is as small as possible. Attacks on these problems usually arrange the spheres so their centers form a lattice. Lattices are described by quadratic forms, and we study the classification of quadratic forms. Most of the book is devoted to these five problems. The miraculous enters: the E 8 and Leech lattices. When we investigate those problems, some fantastic things happen! There are two sphere packings, one in eight dimensions, the E 8 lattice, and one in twenty-four dimensions, the Leech lattice A , which are unexpectedly good and very 24 symmetrical packings, and have a number of remarkable and mysterious properties, not all of which are completely understood even today.
Sphere Packings, Lattices and Groups
Author: John ConwayPublisher: Springer Science & Business Media
ISBN: 1475765681
Category : Mathematics
Languages : en
Pages : 778
Book Description
The third edition of this definitive and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also examine such related issues as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. There is also a description of the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analogue-to-digital conversion and data compression, n-dimensional crystallography, dual theory and superstring theory in physics. New and of special interest is a report on some recent developments in the field, and an updated and enlarged supplementary bibliography with over 800 items.
Report of the National Research Council
Author: National Research Council (U.S.)Publisher:
ISBN:
Category : Research
Languages : en
Pages : 1372
Book Description
History of the Theory of Numbers
Author: Leonard Eugene DicksonPublisher: American Mathematical Soc.
ISBN: 9780821819364
Category : Mathematics
Languages : en
Pages : 324
Book Description
The last volume of Dickson's History is the most modern, covering quadratic and higher forms. The treatment here is more general than in Volume II, which, in a sense, is more concerned with special cases. Indeed, this volume chiefly presents methods of attacking whole classes of problems. Again, Dickson is exhaustive with references and citations.