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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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Power series expansions of Riemann’s $\xi$ function
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by J. B. Keiper PDF
Math. Comp. 58 (1992), 765-773 Request permission

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
  • © Copyright 1992 American Mathematical Society
  • Journal: Math. Comp. 58 (1992), 765-773
  • MSC: Primary 11M06
  • DOI: https://doi.org/10.1090/S0025-5718-1992-1122072-5
  • MathSciNet review: 1122072