## Asymptotic estimates for rational linear spaces on hypersurfaces

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- by Scott T. Parsell PDF
- Trans. Amer. Math. Soc.
**361**(2009), 2929-2957 Request permission

## 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.## References

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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
- 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.
- © Copyright 2009 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**361**(2009), 2929-2957 - MSC (2000): Primary 11D45, 11D72; Secondary 11L07, 11P55
- DOI: https://doi.org/10.1090/S0002-9947-09-04821-1
- MathSciNet review: 2485413