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

 

Power series expansions of Riemann's $ \xi$ function


Author: J. B. Keiper
Journal: Math. Comp. 58 (1992), 765-773
MSC: Primary 11M06
MathSciNet review: 1122072
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Abstract: We show how high-precision values of the coefficients of power series expansions of functions related to Riemann's $ \xi $, function may be calculated. We also show how the Stieltjes constants can be evaluated using this scheme and how the Riemann hypothesis can be expressed in terms of the behavior of two of the sequences of coefficients. High-precision values for the coefficients of these power series are found using Mathematica extsctm.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1992-1122072-5
PII: S 0025-5718(1992)1122072-5
Keywords: Riemann hypothesis, zeta function
Article copyright: © Copyright 1992 American Mathematical Society