منابع مشابه
Quadratic Forms over Arbitrary Fields
Introduction. Witt [5] proved that two binary or ternary quadratic forms, over an arbitrary field (of characteristic not 2) are equivalent if and only if they have the same determinant and Hasse invariant. His proof is brief and elegant but uses a lot of the theory of simple algebras. The purpose of this note is to make this fundamental theorem more accessible by giving a short proof using only...
متن کاملQuadratic Forms over Global Fields
1. The Hasse Principle(s) For Quadratic Forms Over Global Fields 1 1.1. Reminders on global fields 1 1.2. Statement of the Hasse Principles 2 2. The Hasse Principle Over Q 3 2.1. Preliminary Results: Reciprocity and Approximation 3 2.2. n ≤ 1 6 2.3. n = 2 6 2.4. n = 3 6 2.5. n = 4 8 2.6. n ≥ 5 9 3. The Hasse Principle Over a Global Field 9 3.1. n = 2 10 3.2. n = 3 10 3.3. n = 4 11 3.4. n ≥ 5 12...
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 کاملPairs of Quadratic Forms over Finite Fields
Let Fq be a finite field with q elements and let X be a set of matrices over Fq. The main results of this paper are explicit expressions for the number of pairs (A,B) of matrices in X such that A has rank r, B has rank s, and A + B has rank k in the cases that (i) X is the set of alternating matrices over Fq and (ii) X is the set of symmetric matrices over Fq for odd q. Our motivation to study ...
متن کاملPerfect unary forms over real quadratic fields
Let F = Q( √ d) be a real quadratic field with ring of integers O. In this paper we analyze the number hd of GL1(O)orbits of homothety classes of perfect unary forms over F as a function of d. We compute hd exactly for square-free d ≤ 200000. By relating perfect forms to continued fractions, we give bounds on hd and address some questions raised by Watanabe, Yano, and Hayashi.
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: Pacific Journal of Mathematics
سال: 1980
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1980.89.257