FM 99-1 Author: Vieri Mastropietro Title: Anomalous BCS equation for a Luttinger superconductor 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. Keywords: Renormalization group, high T_c superconductivity -------- V.Ma.: Matematica, Universita' di Roma 2, Viale della Ricerca Scientifica, 00133, Roma, Italia. --------- e-mail users: vieri@ipparco.roma1.infn.it, mastropi@axp.mat.utovrm.it tel. 6-72594688