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Let $s_n = \\sigma_n + it_n, \\, t_n >0 $, denote the sequence of nontrivial zeros of the Riemann zeta function in the upper halfplane ordered according to nondecreasing ordinates. We demonstrate that, assuming the Riemann Hypothesis, the Ces\\`{a}ro means of the sequence $F_{s_n} (a)$ converge to the first harmonic $\\exp (2\\pi i a)$ in the sense of periodic distributions. 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