منابع مشابه
Cubic Forms in 14 Variables
The result can be rephrased in geometric language to say that any projective cubic hypersurface defined over Q, of dimension at least 12, has a Q-point. Davenport’s result was extended to arbitrary number fields by Pleasants [9], and it would be interesting to know whether Theorem 1 could similarly be extended. These results can be seen as an attempt to extend the classical theorem of Meyer (18...
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We show that a non-singular integral form of degree d is soluble over the integers if and only if it is soluble over R and over Qp for all primes p, provided that the form has at least (d− 12 √ d)2 variables. This improves on a longstanding result of Birch.
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We define a so-called `-invariant for systems of homogeneous forms of the same degree, which coincides with the well known h-invariant for a single quadratic or cubic form, and bound the `-invariant of a system of rational forms F1, . . . , Fr in terms of the `-invariant of a single form α1F1 + . . . + αrFr in their complex pencil in case of algebraic α1, . . . , αr. As an application, we show ...
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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2019
ISSN: 1435-5345,0075-4102
DOI: 10.1515/crelle-2017-0040