论文标题
二次曲折的对数衍生物的价值分布
Value-Distribution of Logarithmic Derivatives of Quadratic Twists of Automorphic $L$-functions
论文作者
论文摘要
令$ d \ in \ mathbb {n} $，然后让$π$为$ \ mathrm {gl} _ {d}的固定的cuspidal自动形态表示（\ m athbb {a} _ {a} _ {\ mathbb {q}}} $具有单位中心字符。我们确定值$ - \ frac {l'} {l}（1+it，π\ otimesχ_d）$的限制分布为$ d $，而基本判别物也有所不同。在这里，$ t $是一个固定的实际数字，$χ_d$是与$ d $相关的真实字符。我们建立了该家族与其限制分布的融合的差异上的上限。作为此结果的应用，我们获得了$ \ left | \ frac {l'} {l}（1，π\otimesχ_d）\ right | $当$ \ weft | \ frac {l'} {l'} {l'} {l'} {l'} {l'} {1，$π$是自dual时的上限。
Let $d\in\mathbb{N}$, and let $π$ be a fixed cuspidal automorphic representation of $\mathrm{GL}_{d}(\mathbb{A}_{\mathbb{Q}})$ with unitary central character. We determine the limiting distribution of the family of values $-\frac{L'}{L}(1+it,π\otimesχ_D)$ as $D$ varies over fundamental discriminants. Here, $t$ is a fixed real number and $χ_D$ is the real character associated with $D$. We establish an upper bound on the discrepancy in the convergence of this family to its limiting distribution. As an application of this result, we obtain an upper bound on the small values of $\left|\frac{L'}{L}(1,π\otimesχ_D)\right|$ when $π$ is self-dual.
