 

Karl Zimmermann
Commuting polynomials and selfsimilarity


Published: 
March 16, 2007 
Keywords: 
Polynomial, commute, field, root of unity, Chebyshev polynomial 
Subject: 
12Y05 


Abstract
Let F be an algebraically closed field of characteristic 0 and f(x) a polynomial of degree strictly greater than one in F[x]. We show that the number of degree k polynomials with coefficients in F that commute with f (under composition) is either zero or equal to the number of degree one polynomials with coefficients in F that commute with f. As a corollary, we obtain a theorem of E. A. Bertram characterizing those polynomials commuting with a Chebyshev polynomial.


Author information
Department of Mathematics, Union College, Schenectady, NY 12308, USA
zimmermk@union.edu 
