a1 Department of Mathematics, West Chester University, 25 University Ave., West Chester, PA 19383, U.S.A. (email: firstname.lastname@example.org)
We develop Weyl differencing and Hua-type lemmata for a class of multidimensional exponential sums. We then apply our estimates to bound the number of variables required to establish an asymptotic formula for the number of solutions of a system of diophantine equations arising from the study of linear spaces on hypersurfaces. For small values of the degree and dimension, our results are superior to those stemming from the author’s earlier work on Vinogradov’s mean value theorem.
(Received September 06 2011)
(Online publication March 27 2012)
The author is supported in part by National Security Agency Grant H98230-11-1-0190.