I was looking through this paper and I was curious. Has it already been established that the Flint Hills series $\displaystyle\sum_{n\in\mathbb{Z}^{+}}\frac{\csc^2 n}{n^3}$ converges? And has it already been established that the Liouville-Roth irrationality measure of $\pi$ is equal to 2?
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Do you really want the term $n=0$ in there? – GEdgar Jun 08 '19 at 01:38
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2Note that I wrote $n\in\mathbb{Z}^\mathbf{+}$ – Jun 08 '19 at 01:46
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2Flawed, too many mistakes to comment. The "proof" of Lemma 3.1 would imply an explicit upper bound on partial quotients of $\pi$ far below known values. It remains to backtrack it. – metamorphy Jun 08 '19 at 08:15