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Prehomogeneous vector spaces and ergodic theory II
Author(s):
Dave
Witte;
Akihiko
Yukie;
Roger
Zierau
Journal:
Trans. Amer. Math. Soc.
352
(2000),
1687-1708.
MSC (1991):
Primary 11J25;
Secondary 22E30
Posted:
November 17, 1999
MathSciNet review:
1475697
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Abstract:
We apply M. Ratner's theorem on closures of unipotent orbits to the study of three families of prehomogeneous vector spaces. As a result, we prove analogues of the Oppenheim Conjecture for simultaneous approximation by values of certain alternating bilinear forms in an even number of variables and certain alternating trilinear forms in six and seven variables.
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Additional Information:
Dave
Witte
Affiliation:
Department of Mathematics, Oklahoma State University, 401 Math Science, Stillwater, Oklahoma 74078-1058
Email:
dwitte@math.okstate.edu
Akihiko
Yukie
Affiliation:
Department of Mathematics, Oklahoma State University, 401 Math Science, Stillwater, Oklahoma 74078-1058
Address at time of publication:
Mathematical Institute, Tôhoku University, Sendai Miyagi 980-8578, Japan
Email:
yukie@math.tohoku.ac.jp
Roger
Zierau
Affiliation:
Department of Mathematics, Oklahoma State University, 401 Math Science, Stillwater, Oklahoma 74078-1058
Email:
zierau@math.okstate.edu
DOI:
10.1090/S0002-9947-99-02224-2
PII:
S 0002-9947(99)02224-2
Received by editor(s):
May 12, 1997
Posted:
November 17, 1999
Additional Notes:
The first author was partially supported by NSF grant DMS-9214077; the second author was partially supported by NSF grant DMS-9401391; the third author was partially supported by NSF grant DMS-9303224
Copyright of article:
Copyright
2000,
American Mathematical Society
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