An analogue of “Gibbs phenomenon” in the theory of Riemann zeta-function

“Gibbs phenomenon” is well-known in the theory of Fourier series. Roughly speaking, the essence of this phenomenon is that the limit form of plots of partial Fourier sums of the function does not coincide with the plot of limit function near the point of discontinuity. Also, the same effect is well known to the specialists to magnetic resonance imaging as the reason of appearance of false images, and to the specialists to mathematical methods of image processing. Recently, the analogue of this phenomenon was found in the theory of Riemann zeta-function.