Parahoric level $p$-adic $L$-functions for automorphic representations of $\operatorname{GL}_{2n}$ with Shalika models
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908484509892608 |
|---|---|
| author | Dimitrov, Mladen Jorza, Andrei |
| author_facet | Dimitrov, Mladen Jorza, Andrei |
| contents | We construct $p$-adic $L$-functions for regularly refined cuspidal automorphic representations of symplectic type on $\operatorname{GL}_{2n}$ over totally real fields, which are parahoric spherical at every finite place. Furthermore, we prove etaleness of the parabolic eigenvariety at such points and construct $p$-adic $L$-functions in families. The novel local ingredients are the construction of improved Ash--Ginzburg Shalika functionals and production of Friedberg--Jacquet test vectors relating local zeta integrals to automorphic $L$-functions beyond the spherical level. Our proofs rely on a generalization of Shahidi's theory of local coefficients to Shalika models, for which we establish a general factorization formula related to the exterior square automorphic $L$-function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08176 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parahoric level $p$-adic $L$-functions for automorphic representations of $\operatorname{GL}_{2n}$ with Shalika models Dimitrov, Mladen Jorza, Andrei Number Theory We construct $p$-adic $L$-functions for regularly refined cuspidal automorphic representations of symplectic type on $\operatorname{GL}_{2n}$ over totally real fields, which are parahoric spherical at every finite place. Furthermore, we prove etaleness of the parabolic eigenvariety at such points and construct $p$-adic $L$-functions in families. The novel local ingredients are the construction of improved Ash--Ginzburg Shalika functionals and production of Friedberg--Jacquet test vectors relating local zeta integrals to automorphic $L$-functions beyond the spherical level. Our proofs rely on a generalization of Shahidi's theory of local coefficients to Shalika models, for which we establish a general factorization formula related to the exterior square automorphic $L$-function. |
| title | Parahoric level $p$-adic $L$-functions for automorphic representations of $\operatorname{GL}_{2n}$ with Shalika models |
| topic | Number Theory |
| url | https://arxiv.org/abs/2508.08176 |