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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Generic solutions of equations with iterated exponentials


Authors: P. D’Aquino, A. Fornasiero and G. Terzo
Journal: Trans. Amer. Math. Soc. 370 (2018), 1393-1407
MSC (2010): Primary 03C60; Secondary 12L12, 11D61, 11U09
DOI: https://doi.org/10.1090/tran/7206
Published electronically: September 19, 2017
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Abstract: We study solutions of exponential polynomials over the complex field. Assuming Schanuel's Conjecture we prove that certain polynomials of the form

$\displaystyle p(z, e^z, e^{e^z}, e^{e^{e^{z}}}) = 0 $

have generic solutions in $ \mathbb{C}$.

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Additional Information

P. D’Aquino
Affiliation: Dipartimento di Matematica e Fisica, Università della Campania “L. Vanvitelli”, Viale Lincoln 5, 81100 Caserta, Italy
Email: paola.daquino@unicampania.it

A. Fornasiero
Affiliation: Einstein Institute of Mathematics, Edmond J. Safra Campus, The Hebrew University of Jerusalem, Givat Ram, Jerusalem, 9190401, Israel
Email: antongiulio.fornasiero@gmail.com

G. Terzo
Affiliation: Dipartimento di Matematica e Fisica, Università della Campania “L. Vanvitelli”, Viale Lincoln 5, 81100 Caserta, Italy
Email: giuseppina.terzo@unicampania.it

DOI: https://doi.org/10.1090/tran/7206
Keywords: Exponential polynomials, generic solution, Schanuel's Conjecture
Received by editor(s): March 29, 2016
Received by editor(s) in revised form: January 12, 2017
Published electronically: September 19, 2017
Additional Notes: The second author was supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. 291111. This research is part of project FIRB 2010, Nuovi sviluppi nella Teoria dei Modelli dell’esponenziazione.
Article copyright: © Copyright 2017 American Mathematical Society

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