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Asymptotic estimates for rational linear spaces on hypersurfaces
Author(s):
Scott
T.
Parsell
Journal:
Trans. Amer. Math. Soc.
361
(2009),
2929-2957.
MSC (2000):
Primary 11D45, 11D72;
Secondary 11L07, 11P55
Posted:
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:
10.1090/S0002-9947-09-04821-1
PII:
S 0002-9947(09)04821-1
Received by editor(s):
January 8, 2007
Posted:
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.
Copyright of article:
Copyright
2009,
American Mathematical Society
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