Exceptional poles of archimedean Rankin-Selberg L-functions for principal series representations of GL(n,R)
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911621256839168 |
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| author | Jo, Yeongseong Nadimpalli, Santosh Yadav, Akash |
| author_facet | Jo, Yeongseong Nadimpalli, Santosh Yadav, Akash |
| contents | We prove that for any pair of irreducible principal series representations $(π_1,π_2)$ of $\operatorname{GL}_n(\mathbb{R})$ in general position, the notions of exceptional pole of type 1 and type 2 coincide. Using this identification, we express the Rankin--Selberg $L$-function $L(s,π_1\timesπ_2)$ in terms of the exceptional $L$-factors attached to the irreducible constituents of the derivatives of $π_1$ and $π_2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_22259 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exceptional poles of archimedean Rankin-Selberg L-functions for principal series representations of GL(n,R) Jo, Yeongseong Nadimpalli, Santosh Yadav, Akash Number Theory Representation Theory 11F70, 20G20, 22E45 We prove that for any pair of irreducible principal series representations $(π_1,π_2)$ of $\operatorname{GL}_n(\mathbb{R})$ in general position, the notions of exceptional pole of type 1 and type 2 coincide. Using this identification, we express the Rankin--Selberg $L$-function $L(s,π_1\timesπ_2)$ in terms of the exceptional $L$-factors attached to the irreducible constituents of the derivatives of $π_1$ and $π_2$. |
| title | Exceptional poles of archimedean Rankin-Selberg L-functions for principal series representations of GL(n,R) |
| topic | Number Theory Representation Theory 11F70, 20G20, 22E45 |
| url | https://arxiv.org/abs/2604.22259 |