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

DOI:
https://doi.org/10.1090/S0002-9947-99-02224-2

Published electronically:
November 17, 1999

MathSciNet review:
1475697

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9947-99-02224-2

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