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

Abstract

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.

21 pages

References in corpus (1)

• Homogeneous distributions on finite dimensional vector spaces