Asymptotic estimates for rational linear spaces on hypersurfaces

Parsell, Scott

doi:10.1090/S0002-9947-09-04821-1

Asymptotic estimates for rational linear spaces on hypersurfaces
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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.

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