论文标题
DIRICHLET $ L $ functions的对数导数的有条件估计值
Conditional estimates for the logarithmic derivative of Dirichlet $L$-functions
论文作者
论文摘要
假设有一个普遍的Riemann假设，我们在$ Q $中建立了明确的界限，以相机的衍生$ \ left（l'/l \ ry \ right）\ left（σ，χ\右）$ l $ l $ u $ - f unctions $ q $χ$是原始的字符modulo $ q q \ q e qeq 10^$ $ 1/2+1/\ log {\ log {q}} \leqσ\ leq 1-1/\ log \ log q $。此外，对于$σ= 1 $，我们根据Ihara，Murty和Shimura（2009）的结果进行了改进。给出了Riemann Zeta功能的对数衍生物的相似结果。
Assuming the Generalized Riemann Hypothesis, we establish explicit bounds in the $q$-aspect for the logarithmic derivative $\left(L'/L\right)\left(σ,χ\right)$ of Dirichlet $L$-functions, where $χ$ is a primitive character modulo $q\geq 10^{30}$ and $1/2+1/\log{\log{q}}\leqσ\leq 1-1/\log\log q$. In addition, for $σ=1$ we improve upon the result by Ihara, Murty and Shimura (2009). Similar results for the logarithmic derivative of the Riemann zeta-function are given.
