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.