P-ADIC STRING COMPACTIFIED ON A TORUS

U(1)xD model with the Villain action on a g-loop generalization Fg of the Bruhat-Tits tree for the p-adic linear group GL(2, ℚp) is considered. All correlation functions and the statistical sum are calculated. We compute also the averages of these correlation functions for N vertices attached to the boundary of Fg. When the compactification radius tends to infinity the averages provide the g-loop N-point amplitudes of the uncompactified p-adic string theory, in particular for g=0 the Freund-Olson amplitudes. © 1990 Springer-Verlag.