论文标题
在GRH下，$ L $ functions的估算值有效申请
Estimates for $L$-functions in the critical strip under GRH with effective applications
论文作者
论文摘要
假设有一个普遍的Riemann假设，我们为$ \ log {\ Mathcal {\ Mathcal {l}（s）} $和$ \ Mathcal {l}'（s）/\ Mathcal {l}（l}（l} s）$在$ \ Mathcal disem的1线附近（s）$ \ l}（s）的纽约（s）$ \ l}（s）{ Zeta功能。为此，我们将Littlewood众所周知的条件结果推广到具有多项式Euler产品的Selberg类中的功能，为此我们还建立了合适的凸度估计值。作为应用程序，我们为Mertens功能提供有条件有效的估计。
Assuming the Generalized Riemann Hypothesis, we provide explicit upper bounds for moduli of $\log{\mathcal{L}(s)}$ and $\mathcal{L}'(s)/\mathcal{L}(s)$ in the neighbourhood of the 1-line when $\mathcal{L}(s)$ are the Riemann, Dirichlet and Dedekind zeta-functions. To do this, we generalize Littlewood's well known conditional result to functions in the Selberg class with a polynomial Euler product, for which we also establish a suitable convexity estimate. As an application we provide conditional and effective estimate for the Mertens function.
