A NOTE ON HADAMARD ROOTS
OF RATIONAL FUNCTIONS

A.J. VAN DER POORTEN

Abstract:

Suppose F is a polynomial and tex2html_wrap_inline15 represents a rational function. If the tex2html_wrap_inline17 all belong to a field finitely generated over tex2html_wrap_inline19 , then it is a generalization of a conjecture of Pisot that there is a sequence tex2html_wrap_inline21 with tex2html_wrap_inline23 for tex2html_wrap_inline25 so that also tex2html_wrap_inline27 represents a rational function. We explain the context of this Hadamard root conjecture and make some suggestions that might lead to its proof, emphasizing the apparent difficulties that have to be overcome and the ideas that might be employed to that end.