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Journal Articles Mathematics of Computation Year : 2014

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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Dates and versions

inria-00440223 , version 1 (09-12-2009)

Identifiers

  • HAL Id : inria-00440223 , version 1
  • ARXIV : 0912.1927

Cite

Jean-François Biasse. An L(1/3) algorithm for ideal class group and regulator computation in certain number fields. Mathematics of Computation, 2014, 83 (288), pp.2005-2031. ⟨inria-00440223⟩
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