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

Abstract

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

10 pages; referee comments incorporated; to appear in Funct. Approx. Comment. Math