The Sixth Power Moment of Dirichlet L-Functions

We prove a formula, with power savings, for the sixth moment of Dirichlet L- functions averaged over all primitive characters chi (mod q) with q a parts per thousand currency sign Q, and over the critical line. Our formula agrees precisely with predictions motivated by random matrix theory. In particular, the constant 42 appears as a factor in the leading order term, exactly as is predicted for the sixth moment of the Riemann zeta-function.