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 describe a new invariant that we have used to obtain the complete classification of the cubic forms of nine variables. In particular, we compute the covering radius of RM(2, 9) into RM(3, 9).
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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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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2003
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa110-2-3