论文标题
Dirichlet系列具有定期系数及其在关键线附近的价值分布
Dirichlet Series with Periodic Coefficients and their Value-Distribution Near the Critical Line
论文作者
论文摘要
与周期性算术函数相关的Dirichlet系列类别$ f $包括Riemann Zeta功能以及残留类字符的Dirichlet $ L $ functions。我们研究了这些dirichlet系列$ l（s; f）$的价值分布。它们在临界线附近的分析延续（这是相关Riemann-type功能方程的对称性的横坐标）。 In particular, for a fixed complex number $a\neq 0$, we prove for an even or odd periodic $f$ the number of $a$-points of the $Δ$-factor of the functional equation, prove the existence of the mean-value of the values of $L(s;f)$ taken at these points, show that the ordinates of these $a$-points are uniformly distributed modulo one and apply this to show a discrete通用定理。
The class of Dirichlet series associated with a periodic arithmetical function $f$ includes the Riemann zeta-function as well as Dirichlet $L$-functions to residue class characters. We study the value-distribution of these Dirichlet series $L(s;f)$, resp. their analytic continuation in the neighborhood of the critical line (which is the abscissa of symmetry of the related Riemann-type functional equation). In particular, for a fixed complex number $a\neq 0$, we prove for an even or odd periodic $f$ the number of $a$-points of the $Δ$-factor of the functional equation, prove the existence of the mean-value of the values of $L(s;f)$ taken at these points, show that the ordinates of these $a$-points are uniformly distributed modulo one and apply this to show a discrete universality theorem.
