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Preprint Number 686

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686. Vincenzo Mantova (with an Appendix by U. Zannier)
Generic solutions of polynomial exponential equations
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Submission date: 5 February 2014.

Abstract:

We prove that, assuming Schanuel's conjecture, polynomial exponential equations in one variable and with complex coefficients must have generic solutions in the sense of Zilber. With the help of some recent results in Diophantine geometry, we obtain the result by proving that certain polynomial exponential equations have only finitely many rational solutions.
This answers affirmatively to a question of David Marker, who asked (and proved in the case of algebraic coefficients) whether at least the one-variable case of the strong exponential-algebraic closure conjecture, formulated by Zilber, can be reduced to Schanuel's conjecture

Mathematics Subject Classification: 11D61, 03C60

Keywords and phrases:

Full text arXiv: 1402.068: pdf, ps.


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