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Our many-body theory for fractional quantized Hall effect is generalized to include v=qp filling. As the electrons of a two-dimensional system under a strong magnetic field are in a regular array of the Landau orbitals, correlation energy is enhanced and energy gaps are formed. Such a state can give rise to the Hall steps at fractional multiples of e^{2}h. The motion equation of one-particle Green function provides a systematic theory for calculating energy gaps.
R. Tao (Sun,) studied this question.