I've been recently interested in the problem of convergence of the function in such form: $\displaystyle \sum_{n=1}^\infty\frac1{n^p\sin^q n}$.

I saw there's been discussion here when $p=3, q=2$ and $p=2, q=1$ , but wondering if there's any advancement/conclusions in other cases such as $p=3, q=1$ and their potential connection since it's been 11 years for those two posts.

(and also this post also helped my thought)

any relevant paper, article or suggestion will be appreciated. Thanks.