Abstract
In the context of the Anderson theory of high T_c cuprates, we develop a BCS theory for Luttinger liquids. If the Luttinger interaction is much stronger than the BCS potential we find that the BCS equation is quite modified compared to usual BCS equation for Fermi liquids. In particular T_c predicted by the BCS equation for Luttinger liquids is quite higher than the usual T_c for Fermi liquids.
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