Geodesic
Rational approximation and absolute convergence of Fourier series
Sbornik. Mathematics, Tome 35 (1979) no. 4, pp. 509-525 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that if $R_n(f)$ are the smallest uniform deviations of the $2\pi$-periodic function $f$ from rational trigonometric functions of order at most $n$ then the condition $\sum R_n(f)<\infty$ is an unimprovable condition of the absolute convergence of the trigonometric Fourier series of $f$. Bibliography: 20 titles. 
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     title = {Rational approximation and absolute convergence of {Fourier} series},
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E. A. Sevast'yanov. Rational approximation and absolute convergence of Fourier series. Sbornik. Mathematics, Tome 35 (1979) no. 4, pp. 509-525. http://geodesic.mathdoc.fr/item/SM_1979_35_4_a4/

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