On a queer binomial sum

R. Denk and R. Warlimont

Abstract. In this paper the binomial sum

is investigated. It turns out that the behaviour of this sum if n tends to infinity depends on the parameter r and changes dramatically at the values r=1 and r=2. In particular, for r greater or equal to 2  we obtain an oscillatory behaviour while for r<2 the sequence Sn(r) is monotonous at least for large values of n.

Arch. Math. 71 (1998), 22-30.

The paper is available here: pdf