Book Review: Rational quadratic forms
نویسندگان
چکیده
منابع مشابه
On rational quadratic differential forms
In linear system theory, we often encounter the situation of investigating some quadratic functionals which represent Lyapunov functions, energy storage, performance measures, e.t.c. Such a quadratic functional is called a quadratic differential form (QDF) in the context of the behavioral approach. In the past works, a QDF is usually defined in terms of a polynomial matrix. The contribution of ...
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 کاملRational Quadratic Forms and the Local-global Principle
As for most Diophantine equations, quadratic forms were first studied over the integers, meaning that the coefficients aij are integers and only integer values of x1, . . . , xn are allowed to be plugged in. At the end of the 19th century it was realized that by allowing the variables x1, . . . , xn to take rational values, one gets a much more satisfactory theory. (In fact one can study quadra...
متن کاملRational Representations of Primes by Binary Quadratic Forms
Let q be a positive squarefree integer. A prime p is said to be q-admissible if the equation p = u2 + qv2 has rational solutions u, v. Equivalently, p is q-admissible if there is a positive integer k such that pk2 ∈ N , where N is the set of norms of algebraic integers in Q( √ −q). Let k(q) denote the smallest positive integer k such that pk2 ∈ N for all q-admissible primes p. It is shown that ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1980
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1980-14810-7