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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Complex zeros of an incomplete Riemann zeta function and of the incomplete gamma function
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by K. S. Kölbig PDF
Math. Comp. 24 (1970), 679-696 Request permission


Complex zeros of an incomplete Riemann zeta function and of the incomplete gamma function are calculated as functions of the upper limit $\lambda$ 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 $\zeta (s)$ for $\lambda \to \infty$. The remaining trajectories at least in the region considered, approach the zero trajectories of the incomplete gamma function.
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Additional Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Math. Comp. 24 (1970), 679-696
  • MSC: Primary 65.25
  • DOI:
  • MathSciNet review: 0273787