Resumen de Relations between exceptional sets for additive problems

Koichi Kawada, Trevor D. Wooley

• 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(N3/7).