Langlands-shahidi method and poles of automorphicL-functions II

We use Langlands-Shahidi method and the observation that the local components of residual automorphic representations are unitary representations, to study the Rankin-SelbergL-functions of GLk × classical groups. Especially we prove thatL(s, σ ×τ) is holomorphic, except possibly ats=0, 1/2, 1, whereσ is a cuspidal representation of GLk which satisfies weak Ramanujan property in the sense of Cogdell and Piatetski-Shapiro andτ is any generic cuspidal representation of SO2l+1. Also we study the twisted symmetric cubeL-functions, twisted by cuspidal representations of GL2.