Simultaneous integer values of pairs of quadratic forms
نویسندگان
چکیده
منابع مشابه
Simultaneous Integer Values of Pairs of Quadratic Forms
We prove that a pair of integral quadratic forms in 5 or more variables will simultaneously represent “almost all” pairs of integers that satisfy the necessary local conditions, provided that the forms satisfy a suitable nonsingularity condition. In particular such forms simultaneously attain prime values if the obvious local conditions hold. The proof uses the circle method, and in particular ...
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 کاملA Generalized Composition of Quadratic Forms based on Quadratic Pairs
For quadratic spaces which represent 1 there is a characterization of hermitian compositions in the language of algebras-with-involutions using the even Clifford algebra. We extend this notion to define a generalized composition based on quadratic pairs and determine the degrees of minimal compositions for any given quadratic pair.
متن کاملOn Orbits of SL(2,Z)+ and Values of Binary Quadratic Forms on Positive Integral Pairs
We consider actions of SL(2, ZZ) and SL(2, ZZ)+ (semigroup of matrices with nonnegative integral entries) on the projective space IP and on IP × IP . Results are obtained on orbit-closures under these actions and they are applied to describe a class of binary quadratic forms Q such that the sets Q(ZZ2) or Q(ZZ2 +) are dense in IR. We prove also a result generalising a theorem of Troessaert and ...
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: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2017
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crelle-2014-0112