Schanuel's Conjecture and Algebraic Roots of Exponential Polynomials
Logic
2009-10-19 v1 Number Theory
Rings and Algebras
Abstract
In this paper we prove that assuming Schanuel's conjecture, an exponential polynomial in one variable over the algebraic numbers has only finitely many algebraic solutions. This implies a positive answer to Shapiro's conjecture for exponential polynomials over the algebraic numbers for pseudoexponential fields as well as for any algebraically closed exponential field satisfying Schanuel's conjecture.
Keywords
Cite
@article{arxiv.0910.2989,
title = {Schanuel's Conjecture and Algebraic Roots of Exponential Polynomials},
author = {Ahuva C. Shkop},
journal= {arXiv preprint arXiv:0910.2989},
year = {2009}
}