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)).
|Number of pages||22|
|Journal||Journal of the London Mathematical Society|
|Publication status||Published - Oct 2010|
- WARINGS PROBLEM
- HIGHER POWERS