A survey on the evaluation of the values of Dirichlet $L$-functions and of their logarithmic derivatives on the line of $1$
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Speaker:
Sumaia Saad Eddin
Zugehörigkeit:
Johannes Kepler University Linz/MPIM
Datum:
Die, 18/09/2018 - 11:00 - 12:00
Location:
MPIM Lecture Hall 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.
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