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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Complex zeros of an incomplete Riemann zeta function and of the incomplete gamma function


Author: K. S. Kölbig
Journal: Math. Comp. 24 (1970), 679-696
MSC: Primary 65.25
MathSciNet review: 0273787
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1970-0273787-8
PII: S 0025-5718(1970)0273787-8
Keywords: Incomplete Riemann zeta function, incomplete gamma function, complex zeros
Article copyright: © Copyright 1970 American Mathematical Society



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