On the distribution of $\log |L(\sigma ,\chi )|$ and $\log L(\sigma ,{\chi }_D)$ in the modulus aspect

Manami Hosoi, Yumiko Umegaki

Let $\chi$ be a primitive Dirichlet character whose conductor $q$ is a prime number. For the certain averages of values of $\log |L(s,\chi )|$ in $q$-aspect at a fixed $s=\sigma >1/2$, under G…