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Values of decomposable forms at S-integer points and tori orbits on homogeneous spaces

George Tomanov
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Abstract

We classify the closed orbits under the action of maximal tori on the S-adic homogeneous spaces. As an application, we prove that if the set of values at the integer points of any homogeneous non-degenerate split form is discrete, then the form is multiple of a form with rational coefficients. Our result is related to the notable Littlewood conjecture.

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George Tomanov. 2005-07-29. Values of decomposable forms at S-integer points and tori orbits on homogeneous spaces. https://arxiv.org/abs/math/0507613

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