Nonvanishing Twists Of Gl(2) Automorphic L-Functions

Let be a cuspidal automorphic representation of GL(2,AK). Suppose there exists a single non-vanishing nth order twist of the L-series associated to at the center of the critical strip. We use the method of multiple Dirichlet series to establish that there exist infinitely many such non-vanishing nth order twists of the L-series of the representation at the center.