The following is a conjecture due to Littlewood.

> For any set of distinct non-zero integers $n_1,\ldots,n_k$ the inequality
> $$\int_0^{2\pi}|1+e^{in_1x}+\cdots+e^{in_kx}| \, dx\geq C\log k$$  holds.

Has this proven to be true or false?