Oppenheim conjecture for pairs consisting of a linear form and a quadratic form
Author:
Alexander Gorodnik
Translated by:
Journal:
Trans. Amer. Math. Soc. 356 (2004), 4447-4463
MSC (2000):
Primary 11J13, 11H55, 37A17
DOI:
https://doi.org/10.1090/S0002-9947-04-03473-7
Published electronically:
January 13, 2004
MathSciNet review:
2067128
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be a nondegenerate quadratic form and
a nonzero linear form of dimension
. As a generalization of the Oppenheim conjecture, we prove that the set
is dense in
provided that
and
satisfy some natural conditions. The proof uses dynamics on homogeneous spaces of Lie groups.
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Additional Information
Alexander Gorodnik
Affiliation:
Department of Mathematics, Ohio State University, Columbus, Ohio 43210
Address at time of publication:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email:
gorodnik@math.ohio-state.edu, gorodnik@umich.edu
DOI:
https://doi.org/10.1090/S0002-9947-04-03473-7
Received by editor(s):
November 29, 2002
Received by editor(s) in revised form:
May 9, 2003
Published electronically:
January 13, 2004
Additional Notes:
This article is a part of the author’s Ph.D. thesis at Ohio State University done under the supervision of Professor Bergelson
Article copyright:
© Copyright 2004
American Mathematical Society