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

Abstract : 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.
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Contributor : Jean-François Biasse <>
Submitted on : Wednesday, December 9, 2009 - 7:09:45 PM
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  • HAL Id : inria-00440223, version 1
  • ARXIV : 0912.1927

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Jean-François Biasse. An L(1/3) algorithm for ideal class group and regulator computation in certain number fields. Mathematics of Computation, American Mathematical Society, 2014, 83 (288), pp.2005-2031. 〈http://dx.doi.org/10.1090/S0025-5718-2014-02651-3〉. 〈inria-00440223〉

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