Sign change of the function $S(t)$ on short intervals

R. N. Boyarinov

Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2010), pp. 51-53

Résumé

A theorem for the sign change of the argument of the Riemann zeta function $S(t)$ in the interval $(t-A,t+A)$ with $A=4,39\ln\ln\ln\ln T$ for each $t,$ $T\le t\le T+H$, excluding values from the set $E$ with measure ${\rm mes}(E) =O\left(H(\ln\ln T)^{-1}(\ln\ln\ln T)^{-0,5}\right)$ is proved.