Let A be an infinite sequence of positive integers a1 < a2 <... and put fA(x) = Σa∈A, a≤x( 1 a), DA(x) = max1≤n≤xΣa∈A, a n1. In Part I, it was proved that limx→+∞sup DA(x) fA(x) = +∞. In this paper, this theorem is sharpened by estimating DA(x) in terms of fA(x). It is shown that limx→+∞sup DA(x) exp(-c1(logfA(x))2) = +∞ and that this assertion is not true if c1 is replaced by a large constant c2.
ASJC Scopus subject areas
- Algebra and Number Theory