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

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

2005-07-29

arxiv.org/abs/math/0507613v1

Mathematics

Number Theory

26 pages

Scientific paper

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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