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We first review that the holomorphic wave function $f(a)$ can be described in terms of the Jacobi theta functions by imposing gauge invariance on $\\Psi [ a, \\bar{a} ]$ where gauge transformations are induced by doubly periodic translations of $a$. 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We first review that the holomorphic wave function $f(a)$ can be described in terms of the Jacobi theta functions by imposing gauge invariance on $\\Psi [ a, \\bar{a} ]$ where gauge transformations are induced by doubly periodic translations of $a$. 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