On the mean values of Dirichlet L -functions

We study the 2kth power moment of Dirichlet L-functions L(s, χ) at the centre of the critical strip (s = 2 ), where the average is over all primitive characters χ (mod q). We extend to this case the hybrid Euler–Hadamard product results of Gonek, Hughes and Keating for the Riemann zeta function. This allows us to recover conjectures for the moments based on random matrix models, incorporating the arithmetical terms in a natural way.