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Subexponential class group and unit group computation in large degree number fields

Part of: Linear function spaces and their duals Maps and general types of spaces defined by maps Representation theory of groups Birational geometry

Published online by Cambridge University Press:  01 August 2014

Jean-François Biasse  and
Claus Fieker
Jean-François Biasse
Affiliation:
Computer Science Department and Mathematics Department, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada email biasse@lix.polytechnique.fr
Claus Fieker
Affiliation:
University of Kaiserslautern, Fachbereich Mathematik, Postfach 3049, 67653 Kaiserslautern, Germany email fieker@mathematik.uni-kl.de

Abstract

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We describe how to compute the ideal class group and the unit group of an order in a number field in subexponential time. Our method relies on the generalized Riemann hypothesis and other usual heuristics concerning the smoothness of ideals. It applies to arbitrary classes of number fields, including those for which the degree goes to infinity.

MSC classification

Secondary: 54C40: Algebraic properties of function spaces 14E20: Coverings 46E25: Rings and algebras of continuous, differentiable or analytic functions 20C20: Modular representations and characters
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 17 , Special Issue A: Algorithmic Number Theory Symposium XI , 2014 , pp. 385 - 403
Copyright
© The Author(s) 2014 

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