We prove in this thesis three main results, involving the distribution of values of $L'/L(\sigma,\chi_D)$,$D$ being a fundamental discriminant, and $\chi_D$ the real character attached to it. We prove two Omega theorems for $L'/L(1,\chi_D)$, compute the moments of $L'/L(1,\chi_D)$, and construct under GRH, for each $\sigma>1/2$,a density function ${\cal Q}_\sigma$ such that \[\#\{D ~~\text{fundamental discriminants, such that}~~ |D|\leq Y,~~ \text{and}~~ \alpha \leq L'/L(\sigma,\chi_D)\leq \beta \} \]\[ \sim \frac{6}{\pi^2\sqrt{2\pi}} Y \int_\alpha^\beta {\cal Q}_\sigma(x)dx . \]

We prove in this thesis three main results, involving the distribution of values of $L'/L(\sigma,\chi_D)$,$D$ being a fundamental discriminant, and $\chi_D$ the real character attached to it. We prove two Omega theorems for $L'/L(1,\chi_D)$, compute the moments of $L'/L(1,\chi_D)$, and construct under GRH, for each $\sigma>1/2$,a density function ${\cal Q}_\sigma$ such that \[\#\{D ~~\text{fundamental discriminants, such that}~~ |D|\leq Y,~~ \text{and}~~ \alpha \leq L'/L(\sigma,\chi_D)\leq \beta \} \]\[ \sim \frac{6}{\pi^2\sqrt{2\pi}} Y \int_\alpha^\beta {\cal Q}_\sigma(x)dx . \]