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arXiv · 1301.6772

On the representation of quadratic forms by quadratic forms

Rainer Dietmann·Michael Harvey
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Abstract

Using the circle method, we show that for a fixed positive definite integral quadratic form $A$, the expected asymptotic formula for the number of representations of a positive definite integral quadratic form $B$ by $A$ holds true, providing that the dimension of $A$ is large enough in terms of the dimension of $B$ and the maximum ratio of the successive minima of $B$, and providing that $B$ is sufficiently large in terms of $A$.

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Rainer Dietmann, Michael Harvey. 2013-01-28. On the representation of quadratic forms by quadratic forms. https://arxiv.org/abs/1301.6772

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