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Inspired by Sun's breakthrough in establishing the nonvanishing hypothesisfor 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 $\mathrm{GL}_{n} (\mathbbC)\times \mathrm{GL}_n (\mathbb C)$ at the central critical point.

On the nonvanishing hypothesis for Rankin-Selberg convolutions for $\mathrm{GL}_n(\mathbb C)\times \mathrm{GL}_n(\mathbb C)$