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Main Authors: Wei, Zhining, Yang, Liyang, Zhao, Shifan
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2410.09593
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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