Author: Eric Stephen BARNES (and DYER (Henry Peter Francis Swinnerton) Bart.)Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
The Inhomogeneous Minima of Binary Quadratic Forms, Etc
Author: Eric Stephen BARNES (and DYER (Henry Peter Francis Swinnerton) Bart.)Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
The Inhomogeneous Minima of Binary Quadratic Forms
Author: Nigel Christopher BrownPublisher:
ISBN:
Category : Forms, Binary
Languages : en
Pages : 548
Book Description
Isolated Inhomogeneous Minima of Binary Quadratic Forms
Author: Paul M. JenkinsPublisher:
ISBN:
Category : Forms, Binary
Languages : en
Pages : 45
Book Description
The Inhomogeneous Minimum of Indefinite Binary Quadratic Forms with Integer Coefficients
Author: Amikam ZurOn the First Inhomogeneous Minimum of Indefinite Binary Quadratic Forms and Euclid's Algorithm in Real Quadratic Fields
Author: Veikko EnnolaOn the First Inhomogeneous Minimum of Indefinite Binary Quadratic Forms and Euclid's Algorithm in Real Quadratic Fields
Author: Binary Quadratic Forms
Author: Duncan A. BuellPublisher: Springer Science & Business Media
ISBN: 1461245427
Category : Mathematics
Languages : en
Pages : 249
Book Description
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.
An Introduction to the Geometry of Numbers
Author: J.W.S. CasselsPublisher: Springer Science & Business Media
ISBN: 3642620353
Category : Mathematics
Languages : en
Pages : 357
Book Description
From the reviews: "A well-written, very thorough account ... Among the topics are lattices, reduction, Minkowskis Theorem, distance functions, packings, and automorphs; some applications to number theory; excellent bibliographical references." The American Mathematical Monthly
Geometry of Numbers
Author: C. G. LekkerkerkerPublisher: Elsevier
ISBN: 1483259277
Category : Mathematics
Languages : en
Pages : 521
Book Description
Bibliotheca Mathematica: A Series of Monographs on Pure and Applied Mathematics, Volume VIII: Geometry of Numbers focuses on bodies and lattices in the n-dimensional euclidean space. The text first discusses convex bodies and lattice points and the covering constant and inhomogeneous determinant of a set. Topics include the inhomogeneous determinant of a set, covering constant of a set, theorem of Minkowski-Hlawka, packing of convex bodies, successive minima and determinant of a set, successive minima of a convex body, extremal bodies, and polar reciprocal convex bodies. The publication ponders on star bodies, as well as points of critical lattices on the boundary, reducible, and irreducible star bodies and reduction of automorphic star bodies. The manuscript reviews homogeneous and inhomogeneous s forms and some methods. Discussions focus on asymmetric inequalities, inhomogeneous forms in more variables, indefinite binary quadratic forms, diophantine approximation, sums of powers of linear forms, spheres and quadratic forms, and a method of Blichfeldt and Mordell. The text is a dependable reference for researchers and mathematicians interested in bodies and lattices in the n-dimensional euclidean space.
The Minima of Indefinite Quaternary Quadratic Forms ...
Author: Alexander OppenheimPublisher:
ISBN:
Category : Forms, Quadratic
Languages : en
Pages : 76
Book Description