Abstract
We describe a method for bounding the set of exceptional integers not represented by a given additive form in terms of the exceptional set corresponding to a subform. Illustrating our ideas with examples stemming from Waring's problem for cubes, we show, in particular, that the number of positive integers not exceeding N that fail to have a representation as the sum of six cubes of natural numbers is O(N(3/7)).
Original language | English |
---|---|
Pages (from-to) | 437-458 |
Number of pages | 22 |
Journal | Journal of the London Mathematical Society |
Volume | 82 |
DOIs | |
Publication status | Published - Oct 2010 |
Keywords
- WARINGS PROBLEM
- HIGHER POWERS
- SUMS
- CUBES
- IMPROVEMENTS
- SQUARES
- NUMBER