标题： 阿基米德周期关系对于Rankin-Selberg卷积 显示英文标题

标题： Archimedean period relations for Rankin-Selberg convolutions

摘要： 我们阐述并证明了Rankin-Selberg卷积的阿基米德周期关系，针对$\text{GL}(n)\times \text{GL}(n)$和$\text{GL}(n)\times \text{GL}(n-1)$的所有一般上同调表示。 作为推论，我们证明了阿基米德模符号的非零性。 这扩展了[LLS24]中对$\text{GL}(n)\times\text{GL}(n-1)$的本质温度表示的早期结果。 显示英文摘要

摘要： We formulate and prove the archimedean period relations for Rankin-Selberg convolutions of $\text{GL}(n)\times \text{GL}(n)$ and $\text{GL}(n)\times \text{GL}(n-1)$, for all generic cohomological representations. As a consequence, we prove the non-vanishing of the archimedean modular symbols. This extends the earlier results in [LLS24] for essentially tempered representations of $\text{GL}(n)\times\text{GL}(n-1)$.