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.