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Using the correlation function of chiral vertex operators of the Coulomb gasmodel, we find the Laughlin wavefunctions of quantum Hall effect, with fillingfactor $\nu =1/m$, on Riemann sufaces with Poincare metric. The same is donefor quasihole wavefunctions. We also discuss their plasma analogy.Comment: 10 pages, LaTex, the paper is completely rewritten, It will be  appeared in : Jour. Phys. A 32 (1999

Coulomb gas representation of quantum Hall effect on Riemann surfaces