Rational zeros of two quadratic forms
نویسندگان
چکیده
منابع مشابه
Small Zeros of Quadratic Forms
Let N ≥ 2 be an integer, F a quadratic form in N variables over Q, and Z ⊆ Q N an L-dimensional subspace, 1 ≤ L ≤ N . We prove the existence of a small-height maximal totally isotropic subspace of the bilinear space (Z, F ). This provides an analogue over Q of a wellknown theorem of Vaaler proved over number fields. We use our result to prove an effective version of Witt decomposition for a bil...
متن کاملSmall Zeros of Quadratic Forms over Q
Let N ≥ 2 be an integer, F a quadratic form in N variables over Q, and Z ⊆ Q N an L-dimensional subspace, 1 ≤ L ≤ N . We prove the existence of a small-height maximal totally isotropic subspace of the bilinear space (Z, F ). This provides an analogue over Q of a well-known theorem of Vaaler proved over number fields. We use our result to prove an effective version of Witt decomposition for a bi...
متن کاملOn 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 کاملSmall Zeros of Quadratic Forms Outside a Union of Varieties
Let F be a quadratic form in N ≥ 2 variables defined on a vector space V ⊆ KN over a global field K, and Z ⊆ KN be a finite union of varieties defined by families of homogeneous polynomials over K. We show that if V \ Z contains a nontrivial zero of F , then there exists a linearly independent collection of small-height zeros of F in V \ Z, where the height bound does not depend on the height o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1964
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-9-3-261-270