On some sums at the $a$-points of the $k$-th derivatives of the Dirichlet $L$-functions

Authors: MOHAMMED MEKKAOUI, ABDALLAH DERBAL, KAMEL MAZHOUDA

Abstract: Let $L^{(k)}(s,\chi)$ be the $k$-th derivative of the Dirichlet L-function associated with a primitive character $\chi$ mod $q$ and $a$ be a complex number. The solutions of $L^{(k)}(s,\chi)=a$ are called $a$-points. In this paper, we give an asymptotic formula for the sums

Keywords: Dirichlet $L$-function, $a$-points, value-distribution

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