Abstract
AbstractWe investigate the zero sets of complex exponential polynomials in one variable with only one iteration. We characterize when such polynomials have the same zero set in terms of the radical ideals. Moreover we give a bound on the multiplicity of zeros.
Funder
Università degli Studi di Napoli Federico II
Publisher
Springer Science and Business Media LLC
Reference12 articles.
1. D’Aquino, P., Macintyre, A., Terzo, G.: From Schanuel conjecture to shapiro conjecture. Commentarii Mathematicae Elvetici 89(3), 597–616 (2014)
2. Gourin, E.: On irreducible polynomials in several variables which become reducible when the variables are replaced by powers of themselves. Trans. Am. Math. Soc. 32, 485–501 (1930)
3. Henson, C.W., Rubel, L.A.: Some applications of Nevanlinna theory to mathematical logic: identities of exponential functions. Trans. Am. Math. Soc. 282, 1–32 (1984)
4. Katzberg, H.: Complex exponential terms with only finitely many zeros, Seminarberichte, Humboldt-Univ. Berlin. Sekt. Math. 49, 68–72 (1983)
5. MacColl, L.A.: A factorization theory for polynomials in $$x$$ and in functions $$e^{\alpha x}$$. Bull. Am. Math. Soc. 41, 104–109 (1935)