Universality of a non-classical integral quadratic form over Q ( \sqrt 5 )
نویسندگان
چکیده
منابع مشابه
A NON - CLASSICAL QUADRATIC FORM OF HESSIAN DISCRIMINANT 4 IS UNIVERSAL OVER Q ( p 5 )
An adaptation of a quaternionic proof of the Sum of Four Squares Theorem over Q( p 5) is used to show that a particular non-classical quaternary quadratic form is universal.
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The hyperplanes of the symplectic dual polar space DW (5, q) arising from embedding, the so-called classical hyperplanes of DW (5, q), have been determined earlier in the literature. In the present paper, we classify non-classical hyperplanes of DW (5, q). If q is even, then we prove that every such hyperplane is the extension of a non-classical ovoid of a quad of DW (5, q). If q is odd, then w...
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We study codes over a finite field F4. We relate self-dual codes over F4 to real 5-modular lattices and to self-dual codes over F2 via a Gray map. We construct Jacobi forms over Q( √ 5) from the complete weight enumerators of self-dual codes over F4. Furthermore, we relate Hilbert–Siegel forms to the joint weight enumerators of self-dual codes over F4. © 2004 Elsevier Ltd. All rights reserved.
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Let N ≥ 2 be an integer, F a quadratic form in N variables over Q, and Z ⊆ Q N an L-dimensional subspace, 1 ≤ L ≤ N . We prove the existence of a small-height maximal totally isotropic subspace of the bilinear space (Z, F ). This provides an analogue over Q of a well-known theorem of Vaaler proved over number fields. We use our result to prove an effective version of Witt decomposition for a bi...
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Given a polynomial f ∈ Q[X] such that f(Z) ⊂ Z, we investigate whether the set f(Z) can be parametrized by a multivariate polynomial with integer coefficients, that is, the existence of g ∈ Z[X1, . . . , Xm] such that f(Z) = g(Z). We offer a necessary and sufficient condition on f for this to be possible. In particular it turns out that some power of 2 is a common denominator of the coefficient...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2009
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa136-3-3