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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Asymptotic estimates for rational linear spaces on hypersurfaces


Author: Scott T. Parsell
Journal: Trans. Amer. Math. Soc. 361 (2009), 2929-2957
MSC (2000): Primary 11D45, 11D72; Secondary 11L07, 11P55
Published electronically: January 27, 2009
MathSciNet review: 2485413
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Abstract: We develop a repeated efficient differencing procedure for estimating mean values of certain multidimensional exponential sums over smooth numbers. As a consequence, we obtain asymptotic lower bounds for the number of linear spaces of fixed dimension up to a given height lying on the hypersurface defined by an additive equation.


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Additional Information

Scott T. Parsell
Affiliation: Department of Mathematics and Actuarial Science, Butler University, 4600 Sunset Avenue, JH 270, Indianapolis, Indiana 46208
Email: sparsell@butler.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04821-1
PII: S 0002-9947(09)04821-1
Received by editor(s): January 8, 2007
Published electronically: January 27, 2009
Additional Notes: The author was supported in part by a National Science Foundation Postdoctoral Fellowship (DMS-0102068) and by a grant from the Holcomb Research Institute.
Article copyright: © Copyright 2009 American Mathematical Society