On the sign of the real part of the Riemann zeta-function

Juan Arias de Reyna, Richard P. Brent, Jan van de Lune

We consider the distribution of $\arg \zeta (\sigma +it)$ on fixed lines $\sigma >\frac{1}{2}$, and in particular the density \[d(σ) = \lim_{T \rightarrow +\infty} \frac{1}{2T} |\{t \in [-T,+T]: |\argζ…