Hi,

I am trying to put a bound on a sum. Given $\omega=\exp(2\pi i/3)$ and $n$ positive real numbers

$ 0=\tau_0 < \tau_1 < \tau_2 < ...\tau_{n-1}< \tau_n=1 $

such that

$\sum_{i=1}^n\omega^i (\tau_i^m-\tau_{i-1}^m)=0$ for $m=0,1,2,..,N $, what is the upper bound on

$|\sum_{i=1}^n\omega^i (\tau_i^m-\tau_{i-1}^m)|$

for $m >N$?

Thanks.