A hypertrigonometric family of functions expressed using ratios of the Riemann Zeta function.

A hypertrigonometric family of functions bounded by [-1,1] can be defined using ratios of Riemann Zeta functions. Using this approach, the Riemann Zeta critical line zeroes can be understood as finding the minimum of one particular hypertrigonometric function (zetatangent(s)), in the bounded region 0 < = Re ( s ) < = 1, Im(s) > 2π.

可通过黎曼ζ函数（Riemann Zeta）的比值，定义一类值域限制在[-1,1]区间内的超三角函数族。借助该方法，黎曼ζ函数临界线上的零点可被理解为：在实部0≤Re(s)≤1、虚部Im(s)>2π的有界区域内，求取某一特定超三角函数（zetatangent(s)）的极小值。