Schanuel's Conjecture and Algebraic Roots of Exponential Polynomials

Ahuva C. Shkop

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


In this article, I will prove that assuming Schanuel's conjecture, an exponential polynomial with algebraic coefficients can have only finitely many algebraic roots. Furthermore, this proof demonstrates that there are no unexpected algebraic roots of any such exponential polynomial. This implies a special case of Shapiro's conjecture: if p(x) and q(x) are two exponential polynomials with algebraic coefficients, each involving only one iteration of the exponential map, and they have common factors only of the form exp (g) for some exponential polynomial g, then p and q have only finitely many common zeros.

Original languageEnglish
Pages (from-to)3813-3823
Number of pages11
JournalCommunications in Algebra
Issue number10
StatePublished - 1 Oct 2011
Externally publishedYes


  • Exponential algebra
  • Schanuel's conjecture
  • Shapiro's conjecture

ASJC Scopus subject areas

  • Algebra and Number Theory


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