Cohomology classes, periods, and special values of Rankin-Selberg $L$-functions
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911816100085760 |
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| author | Jin, Yubo Yan, Pan |
| author_facet | Jin, Yubo Yan, Pan |
| contents | In this article, we give a cohomological interpretation of (a special case of) the integrals constructed by the second named author and Q. Zhang \cite{YanZhang2023} which represent the product of Rankin-Selberg $L$-functions of $\mathrm{GL}_n\times\mathrm{GL}_m$ and $\mathrm{GL}_n\times\mathrm{GL}_{n-m-1}$ for $m<n$. As an application, we prove an algebraicity result for the special values of certain $L$-functions. This work is a generalization of the algebraicity result of Raghuram for $\mathrm{GL}_n\times\mathrm{GL}_{n-1}$ \cite{Raghuram2010} in the special case $m=n-1$, and the results of Mahnkopf \cite{Mahnkopf1998, Mahnkopf2005} in the special case $m=n-2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18154 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cohomology classes, periods, and special values of Rankin-Selberg $L$-functions Jin, Yubo Yan, Pan Number Theory 11F67, 11F70, 11F75, 22E55 In this article, we give a cohomological interpretation of (a special case of) the integrals constructed by the second named author and Q. Zhang \cite{YanZhang2023} which represent the product of Rankin-Selberg $L$-functions of $\mathrm{GL}_n\times\mathrm{GL}_m$ and $\mathrm{GL}_n\times\mathrm{GL}_{n-m-1}$ for $m<n$. As an application, we prove an algebraicity result for the special values of certain $L$-functions. This work is a generalization of the algebraicity result of Raghuram for $\mathrm{GL}_n\times\mathrm{GL}_{n-1}$ \cite{Raghuram2010} in the special case $m=n-1$, and the results of Mahnkopf \cite{Mahnkopf1998, Mahnkopf2005} in the special case $m=n-2$. |
| title | Cohomology classes, periods, and special values of Rankin-Selberg $L$-functions |
| topic | Number Theory 11F67, 11F70, 11F75, 22E55 |
| url | https://arxiv.org/abs/2403.18154 |