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We put forward the exact version of two-parameter generating functions with$\tau$-invariance, which allows us to give a unified and inherent definitionfor the Drinfeld realization of two-parameter quantum affine algebras for allthe untwisted types. As verification, we first construct their level-one vertexrepresentations of $U_{r,s}(\widehat{\mathfrak{g}})$ for simply-laced types,which in turn well-detect the effectiveness of our definitions both for$(r,s)$-generating functions and $(r,s)$-Drinfeld realization in the frameworkof establishing the two-parameter vertex representation theory.

Generating Functions with $\tau$-Invariance and Vertex Representations  of Quantum Affine Algebras $U_{r,s}(\widehat{\mathfrak{g}})$ (I):  Simply-laced Cases