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High precision computation of a constant in the theory of trigonometric series


Authors: J. Arias de Reyna and J. van de Lune
Journal: Math. Comp. 78 (2009), 2187-2191
MSC (2000): Primary 42-04, 26D05; Secondary 11Y60
DOI: https://doi.org/10.1090/S0025-5718-09-02222-4
Published electronically: February 9, 2009
MathSciNet review: 2521284
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Abstract: Using the bisection as well as the Newton-Raphson method, we compute to high precision the Littlewood-Salem-Izumi constant frequently occurring in the theory of trigonometric sums.


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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

J. van de Lune
Affiliation: Langebuorren 49, 9074 CH Hallum, The Netherlands (formerly at CWI, Amsterdam)
Email: j.vandelune@hccnet.nl

DOI: https://doi.org/10.1090/S0025-5718-09-02222-4
Keywords: Trigonometric sums, Littlewood-Salem-Izumi constant, High precision computation.
Received by editor(s): July 28, 2008
Received by editor(s) in revised form: September 21, 2008
Published electronically: February 9, 2009
Additional Notes: The first author was supported by MCI Grant MTM2006-05622.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.