Title	Unconditional computation of fundamental units in number fields
Creator	Yee, Randy
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2020-05-02T09:51
Description	The current state of the art algorithm for computing a system of fundamental units in a number field without relying on any unproven assumptions or heuristics is due to Buchmann and has an expected run time O(\Delta_K^{1/4 + \epsilon}). If one is willing to assume the GRH, then one can use the index-calculus method, which computes the logarithm lattice corresponding to the unit group. This method has subexponential complexity with respect to the logarithm of the discriminant, though both complexity and correctness of this method depend on the GRH. We discuss a hybrid algorithm which computes the basis of the logarithm lattice for a number field given a full rank sublattice as input. The algorithm is capable of certifying the output of the index calculus algorithm in asymptotically fewer operations than Buchmann's method.
Extent	21.0 minutes
Subject	Mathematics; Mathematics
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: University of Waterloo
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2020-10-30
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0394876
URI	http://hdl.handle.net/2429/76428
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Graduate
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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Unconditional computation of fundamental units in number fields Yee, Randy

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