Complex zeros of two incomplete Riemann zeta functions

Kölbig, K. S.

doi:10.1090/S0025-5718-1972-0303686-6

Complex zeros of two incomplete Riemann zeta functions
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Math. Comp. 26 (1972), 551-565 Request permission

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 $\lambda$ of the definition integral. It becomes apparent that there exist three different classes of zero trajectories for this function, distinguished by their behaviour for $\lambda \to \infty$.

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