Critical convergence and Hausdorff measures for generalized Flint Hills series

We study the generalized Flint Hills series $\mathcal{F}_{s,t}(x)=\sum_{n\ge1} n^{-s}|\sin(πnx)|^{-t}$ for $s>0$ and $t>1$. An explicit comparison with a series over continued-fraction denominators yields the Hausdorff dimension $\min\{1,2t/(s+t)\}$ of its divergence set. At each critical exponent $