Published on *Max Planck Institute for Mathematics* (https://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Sumaia Saad Eddin
Affiliation:

Johannes Kepler University Linz/MPIM
Date:

Tue, 2018-09-18 11:00 - 12:00 Let $q$ be a positive integer $q>1$, and let $\chi$ be a Dirichlet character modulo $q$. Let $L(s, \chi)$ be the attached Dirichlet $L$-functions,

and let $L^\prime(s, \chi)$ denote its derivative with respect to the complex variable $s$. In this talk, we survey certain known results on the evaluation of values of Dirichlet $L$-functions and of their logarithmic derivatives at $1+it_0$ for fixed real number $t_0$.

We also give a new asymptotic formula for the $2k$-th power mean value of $\left|(L^\prime/L)(1+it_0, \chi)\right|$ when $\chi$ runs over all Dirichlet characters modulo $q>1$, for any fixed real number $t_0$. This is joint work with professor Kohji Matsumoto.

**Links:**

[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] https://www.mpim-bonn.mpg.de/node/3444

[3] https://www.mpim-bonn.mpg.de/node/7671