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HUA-TYPE ITERATION FOR MULTIDIMENSIONAL WEYL SUMS
Published online by Cambridge University Press: 27 March 2012
Abstract
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.
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- Copyright © University College London 2012
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