Computing Roots of Truncated Zeta Functions
Greg Fee, SFU
We define the N-term truncated zeta function by the sum of the first N terns of the Riemann zeta function. We use a homotopy method to find some complex roots of a truncated zeta function in a given rectangle. We verify the root count by using Cauchy's integral formula, using numerical quadrature to estimate the integrals along the sides of the the rectangle.