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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 numberfields. Our approach differs from Buchmann-s, who proved a complexity bound ofL1-2,O1 when the discriminant tends to infinity with fixed degree. Weachieve a subexponential complexity in OL1-3,O1 when both thediscriminant and the degree of the extension tend to infinity by usingtechniques due to Enge and Gaudry in the context of algebraic curves overfinite fields.



Author: Jean-François Biasse LIX, INRIA Bordeaux - Sud-Ouest

Source: https://arxiv.org/







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