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arXiv · 2308.12200

Uniform Integrality of critical values of the Rankin-Selberg $L$-function for ${\rm GL}_{n}\times {\rm GL}_{n-1}$

Takashi Hara·Tadashi Miyazaki·Kenichi Namikawa
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Abstract

After introducing the notion of uniform integrality of critical values of the Rankin-Selberg $L$-functions for $\mathrm{GL}_{n}\times \mathrm{GL}_{n-1}$, we study it when the base field is totally imaginary. For this purpose, we adopt specific models of highest weight representations of the general linear groups, construct the Eichler-Shimura classes for $\mathrm{GL}_{n}$ and $\mathrm{GL}_{n-1}$ in an explicit manner, and then evaluate the cohomological cup product of them, by making the best use of Gel'fand-Tsetlin basis.

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Takashi Hara, Tadashi Miyazaki, Kenichi Namikawa. 2023-08-23. Uniform Integrality of critical values of the Rankin-Selberg $L$-function for ${\rm GL}_{n}\times {\rm GL}_{n-1}$. https://arxiv.org/abs/2308.12200

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