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Indefinite quadratic forms and unipotent flows on homogeneous spaces. (English) Zbl 0689.10026

Dynamical systems and ergodic theory, 28th Sem. St. Banach Int. Math. Cent., Warsaw/Pol. 1986, Banach Cent. Publ. 23, 399-409 (1989).
[For the entire collection see Zbl 0686.00015.]
This article contains the proof (using methods from ergodic theory) of Margulis’ celebrated theorem that a real indefinite quadratic form in at least 3 variables that is not proportional to a rational form assumes values arbitrary close to zero.
For related further results and references see S. G. Dani and G. A. Margulis [Invent. Math. 98, No.2, 405-424 (1989)].
Reviewer: R.Schulze-Pillot

MSC:

11D75 Diophantine inequalities
22E40 Discrete subgroups of Lie groups
11E12 Quadratic forms over global rings and fields
11D85 Representation problems

Citations:

Zbl 0686.00015