Prehomogeneous vector spaces and ergodic theory II
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- by Dave Witte, Akihiko Yukie and Roger Zierau PDF
- Trans. Amer. Math. Soc. 352 (2000), 1687-1708 Request permission
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.References
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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
- 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
- © Copyright 2000 American Mathematical Society
- 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
- MathSciNet review: 1475697