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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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Table of 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.