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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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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

Abstract:

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.
References
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Additional Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Math. Comp. 24 (1970), 679-696
  • MSC: Primary 65.25
  • DOI: https://doi.org/10.1090/S0025-5718-1970-0273787-8
  • MathSciNet review: 0273787