Abstract
U(1) xD model with the Villain action on ag-loop generalizationF g of the Bruhat-Tits tree for thep-adic linear groupGL(2, ℚ p ) is considered. All correlation functions and the statistical sum are calculated. We compute also the averages of these correlation functions forN vertices attached to the boundary ofF g. When the compactification radius tends to infinity the averages provide theg-loopN-point amplitudes of the uncompactifiedp-adic string theory, in particular forg=0 the Freund-Olson amplitudes.
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