Polynomial-exponential equations -- some new cases of solvability
Complex Variables
2024-09-27 v2 Logic
Number Theory
Abstract
Recently Brownawell and the second author proved a "non-degenerate" case of the (unproved) "Zilber Nullstellensatz" in connexion with "Strong Exponential Closure". Here we treat some significant new cases. In particular these settle completely the problem of solving polynomial-exponential equations in two complex variables. The methods of proof are also new, as is the consequence, for example, that there are infinitely many complex with .
Cite
@article{arxiv.2303.05592,
title = {Polynomial-exponential equations -- some new cases of solvability},
author = {Vincenzo Mantova and David Masser},
journal= {arXiv preprint arXiv:2303.05592},
year = {2024}
}
Comments
27 pages; added various clarifications; to appear in Proc. Lond. Math. Soc