Products of linear recurring sequences

AbstractLet L(f) denote the space of all sequences of elements of a field F generated by the linear recurrence corresponding to the polynomial f over F. It is well known that if f1, f2,…,fm are polynomials over F none of which has multiple roots, then L(f1) L(f2) … L(fm) = L(h), where h is a polynomial whose roots are the distinct products a1a2…am, ai a root of fi. Here we find such an h in the general case