Omega Theorems for Logarithmic Derivatives of Zeta and L-functions Near the 1-line

We establish an omega theorem for logarithmic derivative of the Riemann zeta function near the 1-line by resonance method. We show that the inequality | ζ^(σA+it)/ζ(σA+it) | ((eA-1)/A)log₂ T + O(log₂ T / log₃ T) has a solution t ∈ [Tβ, T] for all sufficiently large $T,$ where σA = 1 - A / log₂ T.Furthermore, we give a conditional lower bound for the measure of the set of t for which the logarithmic derivative of the Riemann zeta function is large. Moreover, similar results can be generalized to Dirichlet L-functions.