关于Zeta函数零点的运动
On the Motion of Zeros of Zeta Functions
摘要：
在复平面中的运动的零到各种zeta函数的数值研究。首先，赫尔维茨zeta函数被认为是一个精确的公式，其零点的分布建议。然后函数是不同的赫维茨zeta函数的线性组合，并有一个对称分布的零点相对于临界线，进行检查。最后讨论了具有$Re(s)\neq 1/2$的假设非平凡Riemann零点的存在性。
英文摘要：
The motion in the complex plane of the zeros to various zeta functions is investigated numerically. First the Hurwitz zeta function is considered and an accurate formula for the distribution of its zeros is suggested. Then functions which are linear combinations of different Hurwitz zeta functions, and have a symmetric distribution of their zeros with respect to the critical line, are examined. Finally the existence of the hypothetical non-trivial Riemann zeros with $Re(s)\neq 1/2$ is discussed.
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