On the twisted quadratic moment for Dirichlet L-functions
  Given $c,$ a positive integer, we give an explicit formula and an asymptotic formula for \[ \sum\chi(c)|L(1,\,\chi)|^{2}, \] where $\chi$ is the non-trivial Dirichlet character mod $f$ with $f>c.$ 
Seok Hyeong Lee, Seungjai Lee
math.NT