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Mathematics of Computation

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A subquadratic algorithm for computing the $n$-th Bernoulli number

Author: David Harvey
Journal: Math. Comp. 83 (2014), 2471-2477
MSC (2010): Primary 11B68, 11Y55
Published electronically: April 1, 2014
MathSciNet review: 3223342
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Abstract: We describe a new algorithm that computes the $n$th Bernoulli number in $n^{4/3 + o(1)}$ bit operations. This improves on previous algorithms that had complexity $n^{2 + o(1)}$.

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Additional Information

David Harvey
Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia
MR Author ID: 734771
ORCID: 0000-0002-4933-658X

Received by editor(s): October 14, 2012
Received by editor(s) in revised form: February 7, 2013
Published electronically: April 1, 2014
Additional Notes: The author was supported by the Australian Research Council, DECRA Grant DE120101293.
Article copyright: © Copyright 2014 David Harvey