Submission date: 23 January 2013.

Abstract:

Let C be an irreducible algebraic curve defined over a number field and inside an algebraic torus of dimension at least 3. We partially answer a question posed by Levin on points on C for which a non-trivial power lies again on C. Our results have connections to Zilber's Conjecture on Intersections with Tori and yield to methods arising in transcendence theory and the theory of o-minimal structures.

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Full text arXiv 1301.5674: pdf, ps.