New insight into results of Ostrowski and Lang on sums of remainders using Farey sequences

Matthias Kunik

The sums $S(x,t)$ of the centered remainders $kt-\lfloor kt\rfloor -1/2$ over $k\le x$ and corresponding Dirichlet series were studied by A. Ostrowski, E. Hecke, H. Behnke and S…