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.