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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2302.13758 |
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| _version_ | 1866918019317366784 |
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| author | Palacios, Luis Santiago |
| author_facet | Palacios, Luis Santiago |
| contents | Let $K$ be an imaginary quadratic field. In this article, we construct $p$-adic $L$-functions of non-cuspidal Bianchi modular forms by introducing the notions of $C$-cuspidality and partial Bianchi modular symbols. When $p$ splits in $K$, we focus on $p$-adic $L$-functions of non-cuspidal base change Bianchi modular forms, showing that they factor as products of two Katz $p$-adic $L$-functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_13758 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-cuspidal Bianchi modular forms and Katz $p$-adic $L$-functions Palacios, Luis Santiago Number Theory Let $K$ be an imaginary quadratic field. In this article, we construct $p$-adic $L$-functions of non-cuspidal Bianchi modular forms by introducing the notions of $C$-cuspidality and partial Bianchi modular symbols. When $p$ splits in $K$, we focus on $p$-adic $L$-functions of non-cuspidal base change Bianchi modular forms, showing that they factor as products of two Katz $p$-adic $L$-functions. |
| title | Non-cuspidal Bianchi modular forms and Katz $p$-adic $L$-functions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2302.13758 |