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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.23900 |
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Table of 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.