论文标题
使用分数演算与Riemann Zeta函数的零近似
An approximation to zeros of the Riemann zeta function using fractional calculus
论文作者
论文摘要
据作者所知，在本文档中，首次仅使用常数函数的衍生物获得了与Riemann Zeta函数的零的近似值，这仅是因为使用了分数迭代方法。这种迭代方法对一个和几个变量有效，使用了分数演算的属性，特别是，常数的分数衍生物并不总是零，可以使用单个初始条件找到函数的多个零。这部分解决了迭代方法的内在问题，即如果我们想找到n零，则有必要提供N初始条件。因此，该方法适用于近似Riemann Zeta函数的非平凡零，当时其假想部分的绝对值倾向于无穷大。介绍了迭代方法的扣除，其实现的一些示例，最后显示了53个近距离Riemann Zeta函数零的不同值。
In this document, as far as the authors know, an approximation to the zeros of the Riemann zeta function has been obtained for the first time using only derivatives of constant functions, which was possible only because a fractional iterative method was used. This iterative method, valid for one and several variables, uses the properties of fractional calculus, in particular the fact that the fractional derivatives of constants are not always zero, to find multiple zeros of a function using a single initial condition. This partly solves the intrinsic problem of iterative methods that if we want to find N zeros it is necessary to give N initial conditions. Consequently, the method is suitable for approximating nontrivial zeros of the Riemann zeta function when the absolute value of its imaginary part tends to infinity. The deduction of the iterative method is presented, some examples of its implementation, and finally 53 different values near to the zeros of the Riemann zeta function are shown.
