 Amplification polynomial of a multistep method

Applying a linear multistep method to the Dahlquist test equation with $z=h\lambda$ produces a constant-coefficient recurrence whose modes satisfy $P_z(w)=0$. Absolute stability requires the resulting roots of a polynomial to lie in the unit disk, with unit-modulus roots simple. Thus multistep stability depends on every recurrence mode, rather than a single one-step stability function.