Mathematika

Table of Contents - July 2012 - Volume 58, Issue 02  

Research Article

HUA-TYPE ITERATION FOR MULTIDIMENSIONAL WEYL SUMS

Scott T. Parsella1

a1 Department of Mathematics, West Chester University, 25 University Ave., West Chester, PA 19383, U.S.A. (email: sparsell@wcupa.edu)

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.

(Received September 06 2011)

(Online publication March 27 2012)

MSC (2010)

  • 11D45 (primary);
  • 11D72;
  • 11L07;
  • 11L15;
  • 11P55 (secondary)

Footnotes

The author is supported in part by National Security Agency Grant H98230-11-1-0190.