The circle method and bounds for L-functions - IV: Subconvexity for twists of GL(3) L-functions

Let pi be an SL(3, Z) Hecke-Maass cusp form satisfying the Ramanujan conjecture and the Selberg-Ramanujan conjecture, and let chi be a primitive Dirichlet character modulo M, which we assume to be prime for simplicity. We will prove that there is a computable absolute constant delta > 0 such that L(1/2, pi circle times chi) <<(pi) M3/4-5