The dielectric response of a quasi-one-dimensional electron system is studied by including fluctuation effects (in the polarizability) and by using a recently derived analytic form for the electron-electron interactions. General forms for the polarizability matrices both for the intra-and inter-subband cases are presented. The generalized polarizability is analytic over the whole region of the wavevectors artd rigorously retains the number neutrality. Various differences between the intraand

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... er-subband cases for the polarizability and the dielectric matrix function are studied. The theory is used to study impurity screening and plasmon excitations in the presence of multi-subbands. We show that the screened impurity potential of a quasi-one-dimensional electron system is a well defined quantity and, in contrast to its twc-and threedimensional counterparts, it is finite at the origin and has stronger Friedel oscillations. An explanation is given for the experimental results of Hansen et a1 conceming the relationship between the inter-subband plasmon frequencies and the electron densities.