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High precision computation of Riemann's zeta function by the Riemann-Siegel formula, I
Author(s):
J.
Arias
de Reyna.
Journal:
Math. Comp.
80
(2011),
995-1009.
MSC (2010):
Primary 11M06, 11Y35;
Secondary 65E05
Posted:
September 24, 2010
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Abstract:
We present rigorous and sharp bounds for the terms and remainder in the Riemann-Siegel formula (for a general argument, not necessarily on the critical line). This allows for the computation of  and  to high precision. We also derive the Riemann-Siegel formula in a new and more direct way.
References:
-
- 1.
- J. Arias de Reyna, High precision computation of Riemann's Zeta function by the Riemann-Siegel formula, II (to appear).
- 2.
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- 3.
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- 4.
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 first zeros of the Riemann Zeta function, and zeros computation at very large height. http://numbers.computation.free.fr/Constants/Miscellaneous/ zetazeros1e13-1e24.pdf - 7.
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- 9.
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- 10.
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- 11.
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Additional Information:
J.
Arias
de Reyna
Affiliation:
Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, 41080-Sevilla, Spain
Email:
arias@us.es
DOI:
10.1090/S0025-5718-2010-02426-3
PII:
S 0025-5718(2010)02426-3
Received by editor(s):
December 3, 2009
Received by editor(s) in revised form:
February 25, 2010
Posted:
September 24, 2010
Additional Notes:
The author was supported by grant MTM2009-08934.
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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