Zbl.No: 664.10025
where o(1) is a quantity that tends to zero as the number of prime divisors of n tends to infinity. In part I of the present paper [Analytic number theory and diophantine problems, Prog. Math. 70, 1-13 (1987; Zbl 626.10004)] the authors had obtained a similar result but under the stronger hypothesis that 0 \leq h(p) \leq c for some fixed constant c < 1/(k-1).
The proof of (*) rests on a deep theorem of Baranyai on hypergraphs. The authors give heuristic arguments suggesting that (*) remains true with the constant 4+o(1) in place of 2k+o(1) and for any real k \geq 2.
{Note: A result similar to the authors' had been obtained very recently by B. Landreau [C. R. Acad. Sci., Paris, Sér. I 307, No.14, 743- 748 (1988; Zbl 658.10053)].}
Reviewer: A.Hildebrand
Classif.: * 11N37 Asymptotic results on arithmetic functions
11K65 Arithmetic functions (probabilistic number theory)
11A25 Arithmetic functions, etc.
Keywords: divisors; multiplicative function; theorem of Baranyai on hypergraphs
Citations: Zbl 626.10004; Zbl 658.10053
© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag