A two variable Rankin-Selberg integral for $\mathrm{GU}(2,2)$ and the degree 5 $L$-function of $\mathrm{GSp}_4$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913449829728256 |
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| author | Cauchi, Antonio Terradillos, Armando Gutierrez |
| author_facet | Cauchi, Antonio Terradillos, Armando Gutierrez |
| contents | We give a two-variable Rankin--Selberg integral for generic cusp forms on $\mathrm{PGL}_4$ and $\mathrm{PGU}_{2,2}$ which represents a product of exterior square $L$-functions. As a residue of our integral, we obtain an integral representation on $\mathrm{PGU}_{2,2}$ of the degree 5 $L$-function of $\mathrm{GSp}_4$ twisted by the quadratic character of $E/F$ of cuspidal automorphic representations which contribute to the theta correspondence for the pair $(\mathrm{PGSp}_4,\mathrm{PGU}_{2,2})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09855 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A two variable Rankin-Selberg integral for $\mathrm{GU}(2,2)$ and the degree 5 $L$-function of $\mathrm{GSp}_4$ Cauchi, Antonio Terradillos, Armando Gutierrez Number Theory Representation Theory We give a two-variable Rankin--Selberg integral for generic cusp forms on $\mathrm{PGL}_4$ and $\mathrm{PGU}_{2,2}$ which represents a product of exterior square $L$-functions. As a residue of our integral, we obtain an integral representation on $\mathrm{PGU}_{2,2}$ of the degree 5 $L$-function of $\mathrm{GSp}_4$ twisted by the quadratic character of $E/F$ of cuspidal automorphic representations which contribute to the theta correspondence for the pair $(\mathrm{PGSp}_4,\mathrm{PGU}_{2,2})$. |
| title | A two variable Rankin-Selberg integral for $\mathrm{GU}(2,2)$ and the degree 5 $L$-function of $\mathrm{GSp}_4$ |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2402.09855 |