A Note on Divisible Points of Curves
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 nontrivial 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 ominimal structures.
 Publication:

arXiv eprints
 Pub Date:
 January 2013
 arXiv:
 arXiv:1301.5674
 Bibcode:
 2013arXiv1301.5674B
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Logic;
 11G50;
 11J86;
 11U09;
 03C64;
 14H25
 EPrint:
 Published version, but with an error fixed in the formula for the function on page 2