On the invariants of L-functions of degree 2, I: twisted degree and internal shift
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929336204918784 |
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| author | Kaczorowski, J. Perelli, A. |
| author_facet | Kaczorowski, J. Perelli, A. |
| contents | This is the first part of a series of papers where the behaviour of the invariants under twist by Dirichlet characters is studied for $L$-functions of degree 2. Here we show, under suitable conditions, that degree and internal shift remain unchanged under twist. The ultimate goal of the series is to prove a general version of Weil converse theorem with minimal assumptions on the shape of the functional equation of the twists. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_03186 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the invariants of L-functions of degree 2, I: twisted degree and internal shift Kaczorowski, J. Perelli, A. Number Theory 11M41 This is the first part of a series of papers where the behaviour of the invariants under twist by Dirichlet characters is studied for $L$-functions of degree 2. Here we show, under suitable conditions, that degree and internal shift remain unchanged under twist. The ultimate goal of the series is to prove a general version of Weil converse theorem with minimal assumptions on the shape of the functional equation of the twists. |
| title | On the invariants of L-functions of degree 2, I: twisted degree and internal shift |
| topic | Number Theory 11M41 |
| url | https://arxiv.org/abs/2405.03186 |