A simulation study of measurements of neutral current structure functions of the nucleon at the future high-energy and high-luminosity polarized electron-ion collider (EIC) is presented. A new series of $gamma-Z$ interference structure functions, $F_1^{gamma Z}$, $F_3^{gamma Z}$, $g_1^{gamma Z}$, $g_5^{gamma Z}$ become accessible via parity-violating asymmetries in polarized electron-nucleon deep inelastic scattering (DIS). Within the context of the quark-parton model, they provide a unique and, in some cases, yet-unmeasured combination of unpolarized and polarized parton distribution functions. The uncertainty projections for these structure functions using electron-proton collisions are considered for various EIC beam energy configurations. Also presented are uncertainty projections for measurements of the weak mixing angle $sin^2 theta_W$ using electron-deuteron collisions which cover a much higher $Q^2$ than that is accessible in fixed target measurements. QED and QCD radiative corrections and effects of detector smearing are included with the calculations.
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