on the circle whose Fourier series diverges on that set. In French. Sergei Vladimirovich Konyagin, "On divergence of trigonometric Fourier series everywhere", C. R. Acad. Sci. Paris 329 (1999), 693–697. Jean-Pierre Kahane, Some random series of functions, second edition. Cambridge University Press, 1993. The Konyagin paper proves the divergence result discussed above. A simpler proof that gives only log log n can be found in Kahane's book. Fourier series