2009/10/15 by Ahuva C. Shkop, Shkop, Ahuva C.
Mathematics · #03C60 #11U09 #12L12 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Logic (math.LO) #Meromorphic and Entire Functions #Number Theory (math.NT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.0910.2989
openalex publication_date 2009/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.