Solving algebraic equations in roots of unity

Aliev, Iskander ORCID: https://orcid.org/0000-0002-2206-9207 and Smyth, Chris 2012. Solving algebraic equations in roots of unity. Forum Mathematicum 24 (3) , pp. 641-665. 10.1515/form.2011.087

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Abstract

This paper is devoted to finding solutions of polynomial equations in roots of unity. It was conjectured by S. Lang and proved by M. Laurent that all such solutions can be described in terms of a finite number of parametric families called maximal torsion cosets. We obtain new explicit upper bounds for the number of maximal torsion cosets on an algebraic subvariety of the complex algebraic n-torus Gnm . In contrast to earlier work that gives the bounds of polynomial growth in the maximum total degree of defining polynomials, the proofs of our results are constructive. This allows us to obtain a new algorithm for determining maximal torsion cosets on an algebraic subvariety of G nm.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Torsion cosets; roots of unity
Additional Information:	PDF uploaded in accordance with publisher's policies as of 28/07/14.
Publisher:	De Gruyter
ISSN:	1435-5337
Date of First Compliant Deposit:	30 March 2016
Last Modified:	02 May 2023 16:26
URI:	https://orca.cardiff.ac.uk/id/eprint/24970

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