I have seen the occasional reference in literature to the idea that a periodic function is discontinuous iff its Fourier series coefficients $ c_n $ are such that $ c_n \in \mathcal{O}(n^{-1}) $, but this has always been posited without any formal proof or further explanation.
I've tried searching for any further information about this idea, but haven't found anything. Am I being particularly slow, or is this a non-trivial result which requires further proof?
