[en] The low-temperature specific heat for non-magnetic Mg₄₂Y₈Zn₅₀ quasicrystal has been investigated to get information on the electronic structure. The electronic specific heat coefficient γ is estimated to be 0.63 mJ mol^-1 K^-2, which is about 70% of the value expected from the free-electron model. This small γ value strongly suggests the existence of a pseudogap of the electronic density of states in the vicinity of the Fermi level. The low-temperature specific heats of icosahedral Mg₄₂Gd₈Zn₅₀ and Mg₄₂Tb₈Zn₅₀ quasicrystals, which exhibit spin-glass behaviour, have also been investigated. The specific heat of Mg₄₂Gd₈Zn₅₀ exhibits a broad maximum at a temperature that is a few kelvins above the spin freezing temperature T_f determined by AC susceptibility measurements. The magnetic entropy at T_f for the Mg₄₂Gd₈Zn₅₀ quasicrystal reaches about 30% of the theoretical value of R ln 8, being comparable to those of crystalline spin-glass systems such as magnetically dilute AuFe and CuMn alloys. The magnetic specific heat of Mg₄₂Tb₈Zn₅₀ quasicrystal is smaller than that of Mg₄₂Gd₈Zn₅₀, suggesting the splitting of the ground state due to the local electrostatic field. (author)