Ternary universal integral quadratic forms over real quadratic fields
نویسندگان
چکیده
منابع مشابه
Perfect unary forms over real quadratic fields
Let F = Q( √ d) be a real quadratic field with ring of integers O. In this paper we analyze the number hd of GL1(O)orbits of homothety classes of perfect unary forms over F as a function of d. We compute hd exactly for square-free d ≤ 200000. By relating perfect forms to continued fractions, we give bounds on hd and address some questions raised by Watanabe, Yano, and Hayashi.
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Introduction. Witt [5] proved that two binary or ternary quadratic forms, over an arbitrary field (of characteristic not 2) are equivalent if and only if they have the same determinant and Hasse invariant. His proof is brief and elegant but uses a lot of the theory of simple algebras. The purpose of this note is to make this fundamental theorem more accessible by giving a short proof using only...
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ژورنال
عنوان ژورنال: Japanese journal of mathematics. New series
سال: 1996
ISSN: 0289-2316,1861-3624
DOI: 10.4099/math1924.22.263