We see here the graphs of f_{n}(x) for various n.
We introduced the difference sum
f_{n}(x) = S_{[x qn]}(p_{n+1}/q_{n+1}) - S_{[x qn]}(p_{n}/q_{n})in our paper. The p_{n}/q_{n} are the convergents of the rotation number defined by the continued fraction expansion. In our case they are given by Fibonacci numbers. The pictures below show the graphs of the function f_{n} for various n. |