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The density of rational lines on cubic hypersurfaces


Author: Scott T. Parsell
Journal: Trans. Amer. Math. Soc. 352 (2000), 5045-5062
MSC (2000): Primary 11D25, 11D45, 11L03, 11P55
DOI: https://doi.org/10.1090/S0002-9947-00-02635-0
Published electronically: July 18, 2000
MathSciNet review: 1778504
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Abstract | References | Similar Articles | Additional Information

Abstract:

We provide a lower bound for the density of rational lines on the hypersurface defined by an additive cubic equation in at least 57 variables. In the process, we obtain a result on the paucity of non-trivial solutions to an associated system of Diophantine equations.


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Additional Information

Scott T. Parsell
Affiliation: Department of Mathematics, University of Michigan, 525 East University Avenue, Ann Arbor, Michigan 48109-1109
Address at time of publication: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
Email: parsell@alum.mit.edu

DOI: https://doi.org/10.1090/S0002-9947-00-02635-0
Received by editor(s): May 21, 1999
Received by editor(s) in revised form: July 23, 1999
Published electronically: July 18, 2000
Additional Notes: Research supported in part by NSF grant DMS-9622773 and by a fellowship from the David and Lucile Packard Foundation.
Article copyright: © Copyright 2000 American Mathematical Society

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