Estimates are established for the number of integers of size N, in intervals of size N-theta, that fail to admit a representation as the sum of s cubes (s = 5, 6). Thereby it is shown that almost all such integers are represented in the proposed manner. When s = 5 one may take theta = 10/21, and when s = 6 one may take any theta > 17/63. Similar such conclusions are also established for the related problem associated with the expected asymptotic formula.
|Translated title of the contribution||Additive representation in short intervals, I: Waring's problems for cubes|
|Pages (from-to)||1197 - 1220|
|Number of pages||24|
|Publication status||Published - 1 Sep 2004|