Primitive zeros of quadratic forms mod $p^2$
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 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 کاملWitt's Extension Theorem for Mod Four Valued Quadratic Forms
The mod 4 valued quadratic forms defined by E. H. Brown, Jr. are studied. A classification theorem is proven which states that these forms are determined by two things: whether or not their associated bilinear form is alternating, and the rj-invariant of Brown (which generalizes the Arf invariant of an ordinary quadratic form). Particular attention is paid to a generalization of Witt's extensio...
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: Tamkang Journal of Mathematics
سال: 2015
ISSN: 2073-9826,0049-2930
DOI: 10.5556/j.tkjm.46.2015.1745