Period relations for Rankin-Selberg convolutions for $\mathrm{GL}(n)\times \mathrm{GL}(n-1)$

Abstract

We formulate and prove the archimedean period relations for Rankin-Selberg convolutions for $\mathrm{GL}(n)\times \mathrm{GL}(n-1)$. As a consequence, we prove the period relations for critical values of the Rankin-Selberg L-functions for $\mathrm{GL}(n)\times \mathrm{GL}(n-1)$ over arbitrary number fields.