The standard $L$-function attached to a vector valued modular form
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909376287080448 |
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| author | Stein, Oliver |
| author_facet | Stein, Oliver |
| contents | We define two $L$-functions associated to a common vector valued eigenform $f$ transforming with the ``finite'' Weil representation. The first one can be seen as a standard zeta function defined by the eigenvalues of $f$. The second one can be interpreted as standard $L$-function defined as an Euler product where each $p$-factor is a rational function in terms of two unramified characters of the $p$-adic field $\Q_p$. We show that both $L$-functions are related and prove further that they both can be continued meromorphically to the whole complex $s$-plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01620 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The standard $L$-function attached to a vector valued modular form Stein, Oliver Number Theory Functional Analysis We define two $L$-functions associated to a common vector valued eigenform $f$ transforming with the ``finite'' Weil representation. The first one can be seen as a standard zeta function defined by the eigenvalues of $f$. The second one can be interpreted as standard $L$-function defined as an Euler product where each $p$-factor is a rational function in terms of two unramified characters of the $p$-adic field $\Q_p$. We show that both $L$-functions are related and prove further that they both can be continued meromorphically to the whole complex $s$-plane. |
| title | The standard $L$-function attached to a vector valued modular form |
| topic | Number Theory Functional Analysis |
| url | https://arxiv.org/abs/2411.01620 |