On convergence of the Flint Hills series

It is not known whether the Flint Hills series $\sum_{n=1}^{\infty} \frac{1}{n^3\cdot\sin(n)^2}$ converges. We show that this question is closely related to the irrationality measure of $π$, denoted $μ(π)$. In particular, convergence of the Flint Hills series would imply $μ(π) \leq 2.5$ which is much stronger than the best currently known upper bound $μ(π)\leq 7.6063...$. This result easily generalizes to series of the form $\sum_{n=1}^{\infty} \frac{1}{n^u\cdot |\sin(n)|^v}$ where $u,v>0$. We use the currently known bound for $μ(π)$ to derive conditions on $u$ and $v$ that guarantee convergence of such series.

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