Complex symmetric composition operators with automorphic symbols
  In this paper we show that a composition operator $C_\varphi$ cannot be complex symmetric on Hardy-Hilbert space $H^2(D)$ when $\varphi$ is an elliptic automorphism of order $3$ and not a rotation. This completes the project of finding all invertible composition operators which are complex symmetric $H^2(D)$. 
Yong-Xin Gao and Ze-Hua Zhou
math.FA