منابع مشابه
Arithmetic of Quadratic Forms
has a solution in Fn. The representation problem of quadratic forms is to determine, in an effective manner, the set of elements of F that are represented by a particular quadratic form over F . We shall discuss the case when F is a field of arithmetic interest, for instance, the field of complex numbers C, the field of real numbers R, a finite field F, and the field of rational numbers Q. The ...
متن کاملIntroduction to the Arithmetic Theory of Quadratic Forms
1.1. Linear algebra is assumed as a prerequisite to these notes. However, this section serves to review the language of abstract linear algebra (particularly tensor products) for use in the remainder of these notes. We assume the reader familiar with these notions, and therefore do not provide a complete and detailed treatment. In particular, we assume the reader knows what a homomorphism of al...
متن کاملDiophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms
The study of equations over the integers or the rational numbers is the subject of diophantine geometry. This also includes generalizations to finite extensions of the rationals, their rings of integers, and also to function fields over a finite field, and the rings of polynomials therein. This is a vast subject, in which a variety of methods from geometry, analysis, and arithmetic are used. Fo...
متن کاملApplications of quadratic D-forms to generalized quadratic forms
In this paper, we study generalized quadratic forms over a division algebra with involution of the first kind in characteristic two. For this, we associate to every generalized quadratic from a quadratic form on its underlying vector space. It is shown that this form determines the isotropy behavior and the isometry class of generalized quadratic forms.
متن کاملArithmetic Progressions and Binary Quadratic Forms
is a (nonconstant) arithmetic progression of positive integers. We consider a general binary quadratic form ax2 + bxy + cy' ( a , b , c E Z ) and ask the question "Can the form ax' + hxy + ry' represen1 every inleger in 1he arithmetic progression kNo + 1 for any natural numbers k and l?" In a sampling of books containing a discussion of binary quadratic forms [2]-[9], we did not find this qustl...
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ژورنال
عنوان ژورنال: The American Mathematical Monthly
سال: 1951
ISSN: 0002-9890
DOI: 10.2307/2306376