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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Prehomogeneous vector spaces and
ergodic theory II


Authors: Dave Witte, Akihiko Yukie and Roger Zierau
Journal: Trans. Amer. Math. Soc. 352 (2000), 1687-1708
MSC (1991): Primary 11J25; Secondary 22E30
Published electronically: 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: http://dx.doi.org/10.1090/S0002-9947-99-02224-2
PII: S 0002-9947(99)02224-2
Received by editor(s): May 12, 1997
Published electronically: 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
Article copyright: © Copyright 2000 American Mathematical Society