An L(1/3) algorithm for ideal class group and regulator computation in certain number fields
BIASSE, Jean-François
Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
Lithe and fast algorithmic number theory [LFANT]
Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
Lithe and fast algorithmic number theory [LFANT]
BIASSE, Jean-François
Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
Lithe and fast algorithmic number theory [LFANT]
< Reduce
Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
Lithe and fast algorithmic number theory [LFANT]
Language
en
Article de revue
This item was published in
Mathematics of Computation. 2014, vol. 83, n° 288, p. 2005-2031
American Mathematical Society
English 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 ...Read more >
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.Read less <
Origin
Hal imported