Bianchi modular symbols and $p$-adic $L$-functions
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866913388677824512 |
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| author | Kwon, Jaesung |
| author_facet | Kwon, Jaesung |
| contents | In the present paper, we constructed the $p$-adic $L$-function of Bianchi modular form. Also we proved that the first homology groups are generated by the special Bianchi modular symbols. As a corollary, the $μ$-invariant of some isotopic component of the $p$-adic $L$-function vanishes for Bianchi newforms and a positive proportion of ordinary primes. Also we obtain the residual non-vanishing result of the integral $L$-values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_05592 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Bianchi modular symbols and $p$-adic $L$-functions Kwon, Jaesung Number Theory 11F67 11F12 In the present paper, we constructed the $p$-adic $L$-function of Bianchi modular form. Also we proved that the first homology groups are generated by the special Bianchi modular symbols. As a corollary, the $μ$-invariant of some isotopic component of the $p$-adic $L$-function vanishes for Bianchi newforms and a positive proportion of ordinary primes. Also we obtain the residual non-vanishing result of the integral $L$-values. |
| title | Bianchi modular symbols and $p$-adic $L$-functions |
| topic | Number Theory 11F67 11F12 |
| url | https://arxiv.org/abs/2108.05592 |