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 | ^ (A+it) / (A+it) | ( (eA-1) /A) ₂ T + O (₂ T / ₃ T) has a solution t T^, T for all sufficiently large T, where A = 1 - A / ₂ 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.