On values of logarithmic derivative of L-function attached to modular form

This paper aims to initiate a systematic investigation of the distribution of L'/L (1,f,chi), where L(s, f, chi) is the L-function attached to a normalized Hecke eigenform f of weight k for Gamma(0)(N) and chi mod M is a primitive character. Assuming the Riemann hypothesis for L(s, f, chi) and zeta (s), we prove an upper bound of L'/L(1, f, chi) in terms of N, M and k. This result is analogous to that of Ihara, Kumar Murty and Shimura. Next we show that the upper bound is not far from being optimal by proving an unconditional omega result which is analogous to a result of Mourtada and Kumar Murty. In course of proving the omega result, we prove a zero-density estimate for the L-functions involved.