Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Published electronically: July 18, 2000
MathSciNet review: 1778504
Full-text PDF Free Access

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 11D25, 11D45, 11L03, 11P55

Retrieve articles in all journals with MSC (2000): 11D25, 11D45, 11L03, 11P55


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: http://dx.doi.org/10.1090/S0002-9947-00-02635-0
PII: S 0002-9947(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