Critical zeros of Dirichlet $L$-functions
  We use the Asymptotic Large Sieve and Levinson's method to obtain lower bounds for the proportion of simple zeros on the critical line of the twists by primitive Dirichlet characters of a fixed L-function of degree 1,2, or 3. 
Brian Conrey, Henryk Iwaniec, Kannan Soundararajan
math.NT