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COMPARING $\mathbb{C}$ AND ZILBER’S EXPONENTIAL FIELDS: ZERO SETS OF EXPONENTIAL POLYNOMIALS

Part of: Number theory: Connections with logic Model theory

Published online by Cambridge University Press:  04 August 2014

P. D’Aquino ,
A. Macintyre  and
G. Terzo
P. D’Aquino
Affiliation:
Departments of Mathematics and Physics, Seconda Università di Napoli, viale Lincoln 5, 81100 Caserta, Italy (paola.daquino@unina2.it; giuseppina.terzo@unina2.it)
A. Macintyre
Affiliation:
School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, UK (A.Macintyre@qmul.ac.uk)
G. Terzo
Affiliation:
Departments of Mathematics and Physics, Seconda Università di Napoli, viale Lincoln 5, 81100 Caserta, Italy (paola.daquino@unina2.it; giuseppina.terzo@unina2.it)
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Abstract

We continue the research programme of comparing the complex exponential with Zilberś exponential. For the latter, we prove, using diophantine geometry, various properties about zero sets of exponential functions, proved for $\mathbb{C}$ using analytic function theory, for example, the Identity Theorem.

Keywords

exponential fieldsZilber fieldsSchanuel’s ConjectureIdentity Theorem

MSC classification

Primary: 03C60: Model-theoretic algebra 11U09: Model theory
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 15 , Issue 1 , January 2016 , pp. 71 - 84
Copyright
© Cambridge University Press 2014 

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