So, title says it all. Say I have a (complex) series of the form
$$\sum_{n=0}^\infty a_n z^{n^k},$$
for some $k\in \mathbf{N}$.
I'm a little at loss what to do with it to determine its radius of convergence. I can't just apply root test, because that isn't exactly a power series. Then again, I don't think I can just substitute $j = n^k$ (my first idea) and do the tests for the power series
$$\sum_{j=0}^\infty a_{j^{1/k}} z^j,$$
because it wouldn't be the same series; when $j =0, 1, 2, 3, \dots$ $n$ would attain values $n = 0, 1^{1/k}, 2^{1/k}, 3^{1/k}, \dots, (2^k)^{1/k} (= 2), \dots$ instead of $n = 0, 1, 2, 3, \dots$ as in the original series.
I guess there's a critical bit I'm missing. Any hints?