Quadratic forms and systems of forms in many variables
نویسندگان
چکیده
منابع مشابه
Applications 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.
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We generalise Birch’s seminal work on forms in many variables to handle a system of forms in which the degrees need not all be the same. This allows us to prove the Hasse principle, weak approximation, and the Manin–Peyre conjecture for a smooth and geometrically integral variety X ⊆ P, provided only that its dimension is large enough in terms of its degree.
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In this paper, we obtain the upper exponential bounds for the tail probabilities of the quadratic forms for negatively dependent subgaussian random variables. In particular the law of iterated logarithm for quadratic forms of independent subgaussian random variables is generalized to the case of negatively dependent subgaussian random variables.
متن کاملThe moments of products of quadratic forms in normal variables*
The expectation of the product of an arbitrary number of quadratic forms in normally distributed variables is derived.
متن کاملOn Moments of Quadratic Forms in Non-spherically Distributed Variables
We derive the expectations of the matrices xx'" C3 xx' and xx'" C3 xx"' C3 xx.", where C3 denotes a Kronecker product. From this, second and third moments of quadratic forms are obtained. The moments are derived under the following assumption on the product moments of the elements X, of x: For any non-negative integers a,, . . . , ah with C a, 1 6 , E[XE1X2. . . X z ] is i) finite; ii) zero, if...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2018
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-018-0789-x