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Characterization of norm and quasi-norm forms in S-adic setting
George Tomanov
The goal of the present paper is to characterize the norm and quasi-norm forms defined over an arbitrary number field F in terms of their values at the S-integer points, where S is…
Characterization of norm forms via their values at integer points
George Tomanov
Using homogeneous dynamical approach, we obtain a complete description of the forms with discrete set of values at the integer points and not representing zero non-trivially over t…
Values of decomposable forms at S-integer points and tori orbits on homogeneous spaces
George Tomanov
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…
Flows on -arithmetic homogeneous spaces and applications to metric Diophantine approximation
Dmitry Kleinbock, George Tomanov
The main goal of this work is to establish quantitative nondivergence estimates for flows on homogeneous spaces of products of real and -adic Lie groups. These results have appl…