J. Aust. Math. Soc.
76 (2004), 303316

A lightweight version of Waring's problem

Trevor D. Wooley
Department of Mathematics
University of Michigan
East Hall
525 East University Ave
Ann Arbor, MI 481091109
USA
wooley@umich.edu



Abstract

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 deemphasises the large solutions.
Such an asymptotic formula necessarily fails
when this weight is excessively light.

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