BIASSE, Jean-François

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BIASSE, Jean-François
Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
Lithe and fast algorithmic number theory [LFANT]

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Mathematics of Computation. 2014, vol. 83, n° 288, p. 2005-2031

American Mathematical Society

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We analyse the complexity of the computation of the class group structure, regulator, and a system of fundamental units of a certain class of number fields. Our approach differs from Buchmann's, who proved a complexity bound of L(1/2,O(1)) when the discriminant tends to infinity with fixed degree. We achieve a subexponential complexity in O(L(1/3,O(1))) when both the discriminant and the degree of the extension tend to infinity by using techniques due to Enge and Gaudry in the context of algebraic curves over finite fields.< Leer menos

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An L(1/3) algorithm for ideal class group and regulator computation in certain number fields

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