论文标题
Hecke $ l $ form to Angular字符的极端值
Extreme values of Hecke $L$-functions to angular characters
论文作者
论文摘要
令$ k $为一个虚构的二次数字字段，让$ l（s，ξ_ {\ ell}）$表示hecke $ l $ - 函数$ \ ell $。我们检测$ \ log | l（\ tfrac12，ξ_ {\ ell}）| $，其大小至少$ $（\ sqrt {2} + o_k（1））（\ log x / \ log x / \ log \ log x）该结果取决于共振方法，该方法首次应用于这个$ l $ functions的家族，其中对角线术语的分类和提取取决于$ k $的复杂嵌入的几何形状。
Let $K$ be an imaginary quadratic number field and let $L(s,ξ_{\ell})$ denote the Hecke $L$-function to an angular character $ξ_{\ell}$ with frequency $\ell$. We detect values of $\log |L(\tfrac12,ξ_{\ell})|$ with size at least $(\sqrt{2} + o_K(1))(\log X / \log \log X)^{1/2}$ along each dyadic range $X \leqslant \ell \leqslant 2X$. This result relies on the resonance method, which is applied for the first time to this family of $L$-functions, where the classification and extraction of diagonal terms depends on the geometry of the complex embedding of $K$.
