arXiv subjects

Koichi Kawada

Publications and source records attributed to Koichi Kawada.

2 recordsLinked to original sources

arXiv2010

Davenport's method and slim exceptional sets: the asymptotic formulae in Waring's problem

We apply a method of Davenport to improve several estimates for slim exceptional sets associated with the asymptotic formula in Waring's problem. In particular, we show that the anticipated asymptotic formula in Waring's problem for sums of seven cubes holds for all but $O(N^{1/3+ε})$ of the natural numbers not exceeding $N$.

math.NT↗

arXiv2010

Relations between exceptional sets for additive problems

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}).

math.NT↗