Lorentz resonance number and number of poles for Lorentz model

[faryafada]

Hi all
Here, I attached a figure presenting the Lorentz-Drude function. The resonance number is clear from the m in the equation. But I like to know if the number of poles in Lorentz model is the same as the number of resonance or not. I am confused. I would be very grateful if you can help me.
Thanks

 

[Jano L.]

The number of poles is the number of distinct $\omega$ (from complex plane) for which the permitivity diverges. If the divergence occurs, it has to be due to some denominator being zero. Try to count the number of different possibilities.