For which $p>0$ is the series $L^2$-convergent?
$$\sum_{n=1}^ ∞ \frac{1}{n^p}e^ {ix} $$
Now I've been trying to solve this but just cant get the right answer. Another dude on university told me that the answer should be $p>1/2$ and he was pretty sure of it. He told me they couldnt solve it until they got a Theorem that doesnt exist in the "Fourier Analysis.."-book written by Gerald B.Folland.
I did a couple of tries like this but didnt come to anything good. Anyone who think differently and can help me solve this?
