  In this paper we partially settle our conjecture from [1] (math.SP/0701143)
on roots of eigenpolynomials for degenerate exactly-solvable operators. Namely,
for any such operator, we establish a lower bound (which supports our
conjecture) for the largest modulus of the roots of its unique and monic
eigenpolynomial as its degree tends to infinity. The main theorem below thus
extends earlier results obtained in [1] for a more restrictive class of
operators.

Spectral Theory