# Zeros of a Perturbed Polynomial

Zeros of a Perturbed Polynomial

Define the polynomials and (z)=1+z++…+(1+a), , the perturbed polynomial of .

P(z)=1+z++…+

2

z

n

z

P

a

2

z

n

z

a≥0

P(z)

The zeros of and (z) are shown by black and red points, respectively.

P(z)

P

a

The zeros of lie on the unit circle and the zeros of (z) lie inside the unit circle when .

P(z)

P

a

a>0