J. Aust. Math. Soc.  76 (2004), 303-316
A light-weight version of Waring's problem

Trevor D. Wooley
  Department of Mathematics
  University of Michigan
  East Hall
  525 East University Ave
  Ann Arbor, MI 48109-1109

An asymptotic formula is established for the number of representations of a large integer as the sum of kth powers of natural numbers, in which each representation is counted with a homogeneous weight that de-emphasises the large solutions. Such an asymptotic formula necessarily fails when this weight is excessively light.
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