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Solving algebraic equations in roots of unity
-
Iskander Aliev
and
Chris Smyth
Published/Copyright:
May 1, 2012
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 
-torus 
. 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 
.
Keywords: Torsion cosets; roots of unity
Received: 2008-02-01
Revised: 2010-05-12
Published Online: 2012-05-01
Published in Print: 2012-May
© 2012 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- -variable fractals: dimension results
- Maximal function characterizations of Hardy spaces associated with magnetic Schrödinger operators
- Phylogenetic analysis and homology
- Rational homotopy type of the moduli of representations with Borel mold
- Transcendence of special values of quasi-modular forms
- Use of reproducing kernels and Berezin symbols technique in some questions of operator theory
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- Weyl and Zariski chambers on K3 surfaces
- The catenary and tame degree of numerical monoids generated by generalized arithmetic sequences
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