Submission date: 9 March 2023

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 z with e^z+e^{1/z}=1.

Mathematics Subject Classification: 03C60, 14H42, 30C15 (Primary) 32A60, 33E05, 12L12 (Secondary)

Keywords and phrases:

Full text arXiv 2303.05592: pdf, ps.