Generic solutions of equations with iterated exponentials
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- by P. D’Aquino, A. Fornasiero and G. Terzo PDF
- Trans. Amer. Math. Soc. 370 (2018), 1393-1407 Request permission
Abstract:
We study solutions of exponential polynomials over the complex field. Assuming Schanuel’s Conjecture we prove that certain polynomials of the form \[ p(z, e^z, e^{e^z}, e^{e^{e^{z}}}) = 0 \] have generic solutions in $\mathbb C$.References
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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
- MR Author ID: 794986
- Email: antongiulio.fornasiero@gmail.com
- G. Terzo
- Affiliation: Dipartimento di Matematica e Fisica, Università della Campania “L. Vanvitelli”, Viale Lincoln 5, 81100 Caserta, Italy
- MR Author ID: 815935
- Email: giuseppina.terzo@unicampania.it
- 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.
- © Copyright 2017 American Mathematical Society
- 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
- MathSciNet review: 3729505