Non-Vanishing of Cubic Twists of $GL_n(\mathbb{Q})$ $L$-functions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913064093220864 |
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| author | Ghosh, Sayan Mitra, Pratim |
| author_facet | Ghosh, Sayan Mitra, Pratim |
| contents | Let $π$ be an irreducible, cuspidal automorphic representation of $GL_n(\mathbb{A}_\mathbb{Q})$ ($n\geq 3$), which is tempered only for $n=3$. Let $s$ be a complex number such that $\Re(s)\notin \left[1/n, 1-1/n\right]$ if $n\neq 4$; $\Re(s)\notin\left[1/5, 4/5\right]$ if $n=4$, then we show that there are infinitely many primitive cubic Dirichlet characters $χ$ such that $L(s,π\times χ)\neq 0$. Similar results were previously known only for primitive Dirichlet characters without any restriction on the order and quadratic Dirichlet characters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23900 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-Vanishing of Cubic Twists of $GL_n(\mathbb{Q})$ $L$-functions Ghosh, Sayan Mitra, Pratim Number Theory 11M66, 11N36 Let $π$ be an irreducible, cuspidal automorphic representation of $GL_n(\mathbb{A}_\mathbb{Q})$ ($n\geq 3$), which is tempered only for $n=3$. Let $s$ be a complex number such that $\Re(s)\notin \left[1/n, 1-1/n\right]$ if $n\neq 4$; $\Re(s)\notin\left[1/5, 4/5\right]$ if $n=4$, then we show that there are infinitely many primitive cubic Dirichlet characters $χ$ such that $L(s,π\times χ)\neq 0$. Similar results were previously known only for primitive Dirichlet characters without any restriction on the order and quadratic Dirichlet characters. |
| title | Non-Vanishing of Cubic Twists of $GL_n(\mathbb{Q})$ $L$-functions |
| topic | Number Theory 11M66, 11N36 |
| url | https://arxiv.org/abs/2604.23900 |