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Complex Zeros of an Incomplete Riemann Zeta Function and of the Incomplete Gamma Function

K. S. Kölbig
Mathematics of Computation
Vol. 24, No. 111 (Jul., 1970), pp. 679-696
DOI: 10.2307/2004845
Stable URL: http://www.jstor.org/stable/2004845
Page Count: 18
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Complex Zeros of an Incomplete Riemann Zeta Function and of the Incomplete Gamma Function
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Abstract

Complex zeros of an incomplete Riemann zeta function and of the incomplete gamma function are calculated as functions of the upper limit λ of the definition integrals. It becomes apparent that not all, but only some, of the zero trajectories of the incomplete Riemann zeta function join a zero of the Riemann zeta function ζ(s) for λ → ∞. The remaining trajectories at least in the region considered, approach the zero trajectories of the incomplete gamma function.

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