English

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 zz with ez+e1/z=1e^z+e^{1/z}=1.

Keywords

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

R2 v1 2026-06-28T09:10:11.117Z