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Theses

Intégration numérique et calculs de fonctions L

Pascal Molin 1, 2
2 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : This thesis contains a detailed study of the so-called double exponential integration formulas introduced by Takahasi and Mori in 1974, and provides explicit bounds for a rigorous application of the method in number theory. Accurate parameters are given, which makes it possible to use it as a blackbox for the rigorous computation of functions defined by integrals. It also deals with numerical computations of L functions. The complexity of an algorithm due to M. Rubinstein is proven. In the context of double-exponential transformation, a new algorithm is provided whose complexity is low in terms of precision.
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Submitted on : Thursday, November 18, 2010 - 3:47:06 PM
Last modification on : Thursday, January 20, 2022 - 5:31:37 PM
Long-term archiving on: : Friday, October 26, 2012 - 3:56:01 PM

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Pascal Molin. Intégration numérique et calculs de fonctions L. Mathématiques [math]. Université Sciences et Technologies - Bordeaux I, 2010. Français. ⟨tel-00537489⟩

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