Applying the Resonance Method to $\text{Re}(e^{-i\theta }\log \zeta (\sigma +it))$

We apply the resonance method to Montgomery’s convolution formula for $\text{Re}(e^{-i\theta }\log \zeta (\sigma +it))$ in the strip $1\mathrm{/}2<\sigma <1$. This gives new insight into maximal values of $\text{Re}(e^{-i\theta }\log \zeta (\sigma +it))$ for $t\in [T^{\beta },T]$ for all $\beta \in (0,1)$ and real $\theta$.