158,687 research outputs found
Improvements in the computation of ideal class groups of imaginary quadratic number fields
We investigate improvements to the algorithm for the computation of ideal
class groups described by Jacobson in the imaginary quadratic case. These
improvements rely on the large prime strategy and a new method for performing
the linear algebra phase. We achieve a significant speed-up and are able to
compute ideal class groups with discriminants of 110 decimal digits in less
than a week.Comment: 14 pages, 5 figure
Some Results on the Complexity of Numerical Integration
This is a survey (21 pages, 124 references) written for the MCQMC 2014
conference in Leuven, April 2014. We start with the seminal paper of Bakhvalov
(1959) and end with new results on the curse of dimension and on the complexity
of oscillatory integrals. Some small errors of earlier versions are corrected
Computability and analysis: the legacy of Alan Turing
We discuss the legacy of Alan Turing and his impact on computability and
analysis.Comment: 49 page
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