Relations between exceptional sets for additive problems
Number Theory
2015-06-08 v1 Combinatorics
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}).
Cite
@article{arxiv.1001.2495,
title = {Relations between exceptional sets for additive problems},
author = {Koichi Kawada and Trevor D. Wooley},
journal= {arXiv preprint arXiv:1001.2495},
year = {2015}
}