The following is a conjecture due to Littlewood 

For any set of  non-zero integers $n_1,\cdots,n_k$ the inequality
$$\int_0^{2\pi}|1+e^{in_1x}+\cdots+e^{in_kx}|dx\geq C\log k$$ 
holds.
Is this proven to be true(or false)?