Applying the Resonance Method to Re(e-iθlogζ(σ+it))

We apply the resonance method to Montgomery's convolution formula for(e-iθlogζ(σ+it)) in the strip 1/2 < σ < 1. This gives new insight into maximal values of (e-iθlogζ(σ+it)) for t ∈ [Tβ,T] for all β ∈ (0,1) and real θ.