This peak implies the band gap, 2.9, 2.5 and 2.3 eV. The band gap energy decrease, the dielectric constant is increased, recombination rate decrease. This compound is suitable for opto-electronic device.
I suggest you for looking for any possible defects, mainly, on the nano material surfaces. The possible defects might induce the emission peak in the bandgap area.
Furthermore, I do not think that the peaks can be assumed as (fundamental) bandgaps. Additionally, the excitonic states at 350 nm usually screen the transition from HOMO to LUMO, as the fundamental bandgap.