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

 

Some calculations related to Riemann's prime number formula


Authors: Hans Riesel and Gunnar Göhl
Journal: Math. Comp. 24 (1970), 969-983
MSC: Primary 10.41
MathSciNet review: 0277489
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Abstract: The objective of this paper is to study the relation of the complex zeros of the Riemann zeta function to the distribution of prime numbers. This relation arises from a formula of Riemann, which is studied here by extensive machine calculations. To establish the validity of the computations, reasonable upper bounds for the various errors involved are deduced. The analysis makes use of a formula, (32), which seems to be quite new.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1970-0277489-3
PII: S 0025-5718(1970)0277489-3
Keywords: Riemann's prime number formula, zeros of Riemann zeta function, Gram's series
Article copyright: © Copyright 1970 American Mathematical Society