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Complex Zeros of Two Incomplete Riemann Zeta Functions

K. S. Kölbig
Mathematics of Computation
Vol. 26, No. 118 (Apr., 1972), pp. 551-565
DOI: 10.2307/2005183
Stable URL: http://www.jstor.org/stable/2005183
Page Count: 15
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Complex Zeros of Two Incomplete Riemann Zeta Functions
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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 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 → ∞.

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