On the nonvanishing hypothesis for Rankin-Selberg convolutions for   $\mathrm{GL}_n(\mathbb C)\times \mathrm{GL}_n(\mathbb C)$
  Inspired by Sun's breakthrough in establishing the nonvanishing hypothesis for Rankin-Selberg convolutions for the groups $\mathrm{GL}_n (\mathbb R)\times \mathrm{GL}_{n-1} (\mathbb R)$ and $\mathrm{GL}_n (\mathbb C)\times \mathrm{GL}_{n-1} (\mathbb C)$, we confirm it for $\mathrm{GL}_{n} (\mathbb C)\times \mathrm{GL}_n (\mathbb C)$ at the central critical point. 
Chao-Ping Dong and Huajian Xue
math.RT