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Representations of indefinite quadratic forms. (English) Zbl 0883.11016
Let $$f$$ be an integral quadratic form in $$m\geq 3$$ variables and defined over an algebraic number field, and $$g$$ another in $$n$$ variables where $$m\geq n$$ and $$n$$ is arbitrary. Suppose $$f$$ is indefinite. The authors consider the following questions:
(1) How many inequivalent forms in the genus of $$f$$ represent $$g$$ when one knows that at least one form represents $$g$$?
(2) Is there any algebraic structure to the set of forms which represent $$g$$?
These questions were studied previously when the codimension $$\delta: =m-n$$ is greater than or equal to 2, and for the most part when also $$n=1$$. The aim of this paper is to give complete answers to these questions.

##### MSC:
 11E12 Quadratic forms over global rings and fields 11D85 Representation problems
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