发表机构
University of Vienna（维也纳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明在完全分裂素数幂扭下，GL(2) 上尖点形式的特殊 L 值在中心临界点非零，无需类数假设，改进了 Kwon 和 Sun 的结果。
AI 中文摘要
设\u00a0$F$\u00a0为数域，\u00a0$f$\u00a0为\u00a0$F$\u00a0上\u00a0$\mathrm{GL}(2)$\u00a0的归一化尖点 Hecke 特征形式，其\u00a0$L$\u00a0函数\u00a0$L(f,s)$\u00a0的中心临界点为\u00a0$k/2$。设\u00a0$\mathfrak{p}$\u00a0为\u00a0$F$\u00a0中位于奇素数\u00a0$p$\u00a0之上且与\u00a0$f$\u00a0的级理想互素的全分裂素理想。在本文中，我们证明对于\u00a0$F$\u00a0上具有\u00a0$p$\u00a0幂阶和\u00a0$\mathfrak{p}$\u00a0幂导子的充分分歧的 Hecke 特征\u00a0$\phi$，\u00a0$L(f\otimes\phi, k/2)$\u00a0不消失。我们的结果改进了 Jaesung Kwon 和 Hae-Sang Sun 的先前工作，后者需要额外的假设：\u00a0$p$\u00a0不整除\u00a0$F$\u00a0的类数。
英文摘要
Let $F$ be a number field and $f$ a normalized cuspidal Hecke eigenform on $\mathrm{GL}(2)$ over $F$, with $k/2$ as the central critical point of its $L$-function $L(f,s)$. Let $\mathfrak{p}$ be a totally split prime ideal of $F$ lying above an odd prime $p$ and coprime to the level ideal of $f$. In this article, we show that $L(f\otimesϕ, k/2)$ does not vanish for sufficiently ramified Hecke characters of $F$ of $p$-power order and $\mathfrak{p}$-power conductor. Our result improves previous works of Jaesung Kwon and Hae-Sang Sun, in which the additional hypothesis that $p$ does not divide the class number of $F$ is required.
Comments21 pages. Comments welcome!
