论文标题
Riemann型功能方程 - 朱莉娅线和计数公式 -
Riemann-Type Functional Equations -- Julia Line and Counting Formulae --
论文作者
论文摘要
我们研究了关于价值分布理论的Riemann型功能方程，并对其解决方案产生了影响。特别是，对于固定的复数$ a \ neq0 $和Selberg类$ \ Mathcal {l} $的功能，我们证明了Riemann-Von Mangoldt公式，用于$ \ \ \ \ \ \ Mathcal {l} $和landau的形式的$Δ$比例的A-Points的数量从最后一个公式开始，我们得出这些$ a $ points的尺寸是均匀分布的modulo One。最后，我们展示了在这些点所取的$ \ Mathcal {l}（s）$的值的均值。
We study Riemann-type functional equations with respect to value-distribution theory and derive implications for their solutions. In particular, for a fixed complex number $a\neq0$ and a function from the Selberg class $\mathcal{L}$, we prove a Riemann-von Mangoldt formula for the number of a-points of the $Δ$-factor of the functional equation of $\mathcal{L}$ and an analog of Landau's formula over these points. From the last formula we derive that the ordinates of these $a$-points are uniformly distributed modulo one. Lastly, we show the existence of the mean-value of the values of $\mathcal{L}(s)$ taken at these points.
