A local converse theorem for U(1,1)

In this paper, we define a gamma-factor for generic representations of U(1, 1) xRes(E/F) (GL(1)) and prove a local converse theorem for U(1, 1) using the gamma-factor we defined. We also give a new proof of the local converse theorem for GL(2) using a gamma-factor of GL(2) x GL(2) type which was originally defined by Jacquet in [Automorphic Forms on GL(2), Part 2, Springer Lecture Notes in Mathematics, Vol. 278 (Springer, 1972)].