Rational approximation and absolute convergence of Fourier series

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 $f$.
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