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arXiv · 2412.18805

Archimedean period relations for Rankin-Selberg convolutions

Yubo Jin·Dongwen Liu·Binyong Sun
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Abstract

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 $\text{GL}(n)\times\text{GL}(n-1)$.

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Yubo Jin, Dongwen Liu, Binyong Sun. 2024-12-25. Archimedean period relations for Rankin-Selberg convolutions. https://arxiv.org/abs/2412.18805

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