let-f-C-R-z-min-y-y-y-1-y-y-Im-z-let-w-e-i-2pi-n-n-N-evaluate-S-n-0-k-lt-n-f-w-k-

Question Number 157593 by metamorfose last updated on 25/Oct/21

l e t f : C \to R

z \to m i n (y - [y], [y + 1] - y), y = I m (z)

l e t w = e^{i \frac{2 π}{n}}, n \in N^{*}

e v a l u a t e S_{n} = \sum_{0 ⩽ k < n} f (w^{k})