The numerator of a filter modifies the signal in the frequency domain. On the other hand, the numerator denotes the zeros of a transfer function.
Poles of a transfer function tell us about the cut-off frequency of a filter.
Process of finding the cut-off frequency of a filter from z-transform
Let's assume the transfer function of a filter, H(z) = 1 / {1 - a*z^(-1)}
Where a is a constant. This represents a simple first-order recursive (IIR) low-pass filter
Then, make dominator, 1 - a*z^(-1) = 0
Or, z = a
Then calculate the magnitude of the pole: |a|
If |a| is close to 1, then it is closest to the unit circle
The cut-off frequency in radians is determined by the angle θ between the real axis and the line connecting 0 to the pole a
and θ = arctan{imag(a) / real(a)}