Generic solutions of equations with iterated exponentials

TL;DR

This paper investigates solutions to exponential polynomial equations over complex numbers, demonstrating that, assuming Schanuel's conjecture, certain polynomials possess generic solutions in the complex field.

Contribution

The paper provides a conditional proof that specific exponential polynomials have generic solutions, advancing understanding of solutions under Schanuel's conjecture.

Findings

Conditional proof of existence of generic solutions

Identification of classes of exponential polynomials with solutions

Progress towards understanding exponential polynomial solutions

Abstract

We study solutions of exponential polynomials over the complex field. Assuming Schanuel's conjecture we prove that certain polynomials have generic solutions in the complex field.