Consider $f_n(t)=\sum_{i=1}^{n}e^{ik_{i}t}$ with all $k_i$ some distinct integers for $t\in [-\pi,\pi)$. For $p>2$ I am interested in the maximum possible value of $$||f_n||_p,$$ where $f_n$ runs through all possible such sums with $n$ terms. Of particular interest is the case when $p$ is an even integer and $n\rightarrow \infty$ in case obtaining the sharp upper bound is too ambitious. Could it be that the Dirichlet kernel is the best such $f_n$?