Relative Trace Formula and Uniform non-vanishing of Central $L$-values of Hilbert Modular Forms
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914970577403904 |
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| author | Wei, Zhining Yang, Liyang Zhao, Shifan |
| author_facet | Wei, Zhining Yang, Liyang Zhao, Shifan |
| contents | Let $\mathcal{F}(\mathbf{k},\mathfrak{q})$ be the set of normalized Hilbert newforms of weight $\mathbf{k}$ and prime level $\mathfrak{q}$. In this paper, utilizing regularized relative trace formulas, we establish a positive proportion of $\#\{π\in\mathcal{F}(\mathbf{k},\mathfrak{q}):L(1/2,π)\neq 0\}$ as $\#\mathcal{F}(\mathbf{k},\mathfrak{q})\to+\infty$. Moreover, our result matches the strength of the best known results in both the level and weight aspects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09593 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relative Trace Formula and Uniform non-vanishing of Central $L$-values of Hilbert Modular Forms Wei, Zhining Yang, Liyang Zhao, Shifan Number Theory Let $\mathcal{F}(\mathbf{k},\mathfrak{q})$ be the set of normalized Hilbert newforms of weight $\mathbf{k}$ and prime level $\mathfrak{q}$. In this paper, utilizing regularized relative trace formulas, we establish a positive proportion of $\#\{π\in\mathcal{F}(\mathbf{k},\mathfrak{q}):L(1/2,π)\neq 0\}$ as $\#\mathcal{F}(\mathbf{k},\mathfrak{q})\to+\infty$. Moreover, our result matches the strength of the best known results in both the level and weight aspects. |
| title | Relative Trace Formula and Uniform non-vanishing of Central $L$-values of Hilbert Modular Forms |
| topic | Number Theory |
| url | https://arxiv.org/abs/2410.09593 |