DISTRIBUTION OF VALUES OF L′/L(σ, χD)

We study the distribution of values of I L (sigma, chi(D)) where sigma is real > 1/2 a fundamental discriminant, and chi(D) the real character attached to D In particular, assuming the GRH, we prove that for each sigma > 1/2 there is a density function Q(sigma) with the property that for real numbers alpha <= beta, we have #{D fundamental discriminants such that vertical bar D vertical bar <= Y, and alpha <= L'/L (sigma, chi(D)) <= beta} similar to 6/pi(2)root 2 pi Y integral(beta)(alpha) Q(sigma)(x)dx. Our work is based on and strongly motivated by the earlier work of Ihara and 'Matsumoto [7].