Complex zeros of two incomplete Riemann zeta functions

Abstract

The computation of the complex zeros of an incomplete Riemann zeta function defined in an earlier paper is extended and new zero trajectories are given. A second incomplete Riemann zeta function is defined and its zero trajectories are investigated numerically as functions of the upper limit λ \lambda of the definition integral. It becomes apparent that there exist three different classes of zero trajectories for this function, distinguished by their behaviour for λ → ∞ \lambda \to \infty .