Geodesic
On divergence sets for trigonometric Fourier series
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (1982), pp. 11-16

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There exists $f(x)\in C[0,2\pi]$, with the following condition. If $E$ is the divergence set for the trigonometric Fourier series of $f(x)$ then $E\in G_{\delta\sigma}$, $E\notin F_\sigma$, $E\notin G_\delta$. 
@article{VMUMM_1982_3_a2,
     author = {S. Yu. Lukashenko},
     title = {On divergence sets for trigonometric {Fourier} series},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {11--16},
     publisher = {mathdoc},
     number = {3},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1982_3_a2/}
}
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S. Yu. Lukashenko. On divergence sets for trigonometric Fourier series. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (1982), pp. 11-16. http://geodesic.mathdoc.fr/item/VMUMM_1982_3_a2/