Sign Change of the Function S(t) on Short Intervals / Boyarinov R.N. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2010. ? 3. P. 51-53 [Moscow Univ. Math. Bulletin. Vol. 65, No 3, 2010. P. 132-134].

A theorem for the sign variation of the argument of the Riemann zeta function S(t) in the interval (t-A, t+A) with A=4,39ln ln ln ln T for each t, T ≤ t ≤ T+H excluding values from the set E with the measure mes(E) = O(H(ln ln T)^-1(ln ln ln T)^-0,5) is proved.

Key words: argument of the Riemann zeta function, Selberg's approximate formula.