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Complex zeros of two incomplete Riemann zeta functions


Author: K. S. KΓΆlbig
Journal: Math. Comp. 26 (1972), 551-565
MSC: Primary 65D20
DOI: https://doi.org/10.1090/S0025-5718-1972-0303686-6
MathSciNet review: 0303686
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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 $ \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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DOI: https://doi.org/10.1090/S0025-5718-1972-0303686-6
Keywords: Incomplete Riemann zeta function, incomplete gamma function, Debye function, complex zeros
Article copyright: © Copyright 1972 American Mathematical Society

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