On the nonvanishing hypothesis for Rankin-Selberg convolutions for 𝐺𝐿_{𝑛}(ℂ)×𝔾𝕃_{𝕟}(ℂ)

Abstract

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