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

Inspired by Sun’s breakthrough in establishing the nonvanishing hypothesis for Rankin-Selberg convolutions for the groups $$\mathrm{G}\mathrm{L}$n (\mathbb R)\times $\mathrm{G}\mathrm{L}${n-1} (\mathbb R)$and$$\mathrm{G}\mathrm{L}$n (\mathbb C)\times $\mathrm{G}\mathrm{L}${n-1} (\mathbb C)$,weconfirmitfor$$\mathrm{G}\mathrm{L}$_{n} (\mathbb C)\times $\mathrm{G}\mathrm{L}$_n (\mathbb C)$ at the central critical point.