Polynomial-exponential equations -- some new cases of solvability

Fuente: arXiv
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Main Authors: Mantova, Vincenzo, Masser, David
Format: Preprint
Published: 2023
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author Mantova, Vincenzo
Masser, David
author_facet Mantova, Vincenzo
Masser, David
contents 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 $e^z+e^{1/z}=1$.
format Preprint
id arxiv_https___arxiv_org_abs_2303_05592
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Polynomial-exponential equations -- some new cases of solvability
Mantova, Vincenzo
Masser, David
Complex Variables
Logic
Number Theory
03C60, 14H42, 30C15 (Primary) 32A60, 33E05, 12L12 (Secondary)
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 $e^z+e^{1/z}=1$.
title Polynomial-exponential equations -- some new cases of solvability
topic Complex Variables
Logic
Number Theory
03C60, 14H42, 30C15 (Primary) 32A60, 33E05, 12L12 (Secondary)
url https://arxiv.org/abs/2303.05592