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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.02607 |
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| _version_ | 1866918163543752704 |
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| author | Knospe, Heiko Dąbrowski, Andrzej |
| author_facet | Knospe, Heiko Dąbrowski, Andrzej |
| contents | We investigate the twisting of motivic $L$-functions by a family of multiplicative characters $ψ$, defined on prime ideals $\mathfrak{p}$ via $ψ(\mathfrak{p})=α^{N(\mathfrak{p})}$ for a fixed $α\in \mathbb{C}$. One can extend $ψ$ to a continuous non-Hecke character on the idele group of a number field. For $|α|<1$, the resulting $ψ$-twisted $L$-function has interesting analytic properties: an enhanced half-plane of absolute convergence, preservation of the Euler product structure, and meromorphic continuation to the complex plane. We give applications to Dirichlet $L$-functions and $L$-functions associated to modular forms. Furthermore, we show that $ψ$-twisting allows the construction of convergent $p$-adic Dirichlet series and $p$-adic Euler products which have some similarities with their complex counterparts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02607 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a multiplicative non-Hecke twist of motivic L-functions Knospe, Heiko Dąbrowski, Andrzej Number Theory 11R42 (Primary) 11M41, 11R23, 11S80 (Secondary) We investigate the twisting of motivic $L$-functions by a family of multiplicative characters $ψ$, defined on prime ideals $\mathfrak{p}$ via $ψ(\mathfrak{p})=α^{N(\mathfrak{p})}$ for a fixed $α\in \mathbb{C}$. One can extend $ψ$ to a continuous non-Hecke character on the idele group of a number field. For $|α|<1$, the resulting $ψ$-twisted $L$-function has interesting analytic properties: an enhanced half-plane of absolute convergence, preservation of the Euler product structure, and meromorphic continuation to the complex plane. We give applications to Dirichlet $L$-functions and $L$-functions associated to modular forms. Furthermore, we show that $ψ$-twisting allows the construction of convergent $p$-adic Dirichlet series and $p$-adic Euler products which have some similarities with their complex counterparts. |
| title | On a multiplicative non-Hecke twist of motivic L-functions |
| topic | Number Theory 11R42 (Primary) 11M41, 11R23, 11S80 (Secondary) |
| url | https://arxiv.org/abs/2508.02607 |