Critical convergence and Hausdorff measures for generalized Flint Hills series

Yuya Dan

We study the generalized Flint Hills series ${\mathcal{F}}_{s,t}(x)={\sum }_{n\ge 1}{n}^{-s}|\sin (\pi nx){|}^{-t}$ for $s>0$ and $t>1$. An explicit comparison with a series over continued-frac…