Anticyclotomic $p$-adic $L$-functions for Coleman families of $U_{n+1} \times U_{n}$
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916310088155136 |
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| author | Dimitrakopoulou, Xenia |
| author_facet | Dimitrakopoulou, Xenia |
| contents | By $p$-adically interpolating the branching law for the spherical pair $\left(U_n, U_{n+1} \times U_{n}\right)$ of definite unitary groups, we construct a $p$-adic $L$-function attached to cohomological automorphic representations of $U_{n+1} \times U_{n}$. Under a further multiplicity one assumption, we extend the construction to Coleman families. Our $p$-adic $L$-function interpolates the square root of the central critical $L$-value. It has weight and anticyclotomic variables and its construction relies on the proof of the unitary Gan--Gross--Prasad conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_05841 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Anticyclotomic $p$-adic $L$-functions for Coleman families of $U_{n+1} \times U_{n}$ Dimitrakopoulou, Xenia Number Theory By $p$-adically interpolating the branching law for the spherical pair $\left(U_n, U_{n+1} \times U_{n}\right)$ of definite unitary groups, we construct a $p$-adic $L$-function attached to cohomological automorphic representations of $U_{n+1} \times U_{n}$. Under a further multiplicity one assumption, we extend the construction to Coleman families. Our $p$-adic $L$-function interpolates the square root of the central critical $L$-value. It has weight and anticyclotomic variables and its construction relies on the proof of the unitary Gan--Gross--Prasad conjecture. |
| title | Anticyclotomic $p$-adic $L$-functions for Coleman families of $U_{n+1} \times U_{n}$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2312.05841 |