Mantova, V orcid.org/0000-0002-8454-7315 and Zannier, U (2016) Polynomial–exponential equations and Zilber's conjecture. Bulletin of the London Mathematical Society, 48 (2). pp. 309-320. ISSN 0024-6093
Abstract
Assuming Schanuel's conjecture, we prove that any polynomial–exponential equation in one variable must have a solution that is transcendental over a given finitely generated field. With the help of some recent results in Diophantine geometry, we obtain the result by proving (unconditionally) that certain polynomial–exponential equations have only finitely many rational solutions. This answers affirmatively a question of David Marker, who asked, and proved in the case of algebraic coefficients, whether at least the one variable case of Zilber's strong exponential-algebraic closedness conjecture can be reduced to Schanuel's conjecture.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2016, Wiley. This is an author produced version of a paper published in Bulletin of the London Mathematical Society . Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 04 May 2017 11:08 |
Last Modified: | 02 Jul 2017 20:29 |
Published Version: | https://doi.org/10.1112/blms/bdv096 |
Status: | Published |
Publisher: | Wiley |
Identification Number: | 10.1112/blms/bdv096 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:115288 |