Abstract
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 |
|---|---|
| Original language | English |
| Pages (from-to) | 1197 - 1220 |
| Number of pages | 24 |
| Journal | Compositio Mathematica |
| Volume | 140 (5) |
| DOIs | |
| Publication status | Published - 1 Sept 2004 |