Singularities of adelic Feynman amplitudes

We study adelic phi (4)-theory with propagator, given by homogeneous adelic function. It is shown that almost all ultraviolet and infrared poles of Eu clidean Feynman amplitude are cancelled by zeroes of the infinite product o f p-adic Feynman amplitudes. Analytic continuation in the degree of homogen eity of general adelic Feynman amplitude is constructed. We prove that all adelic phi (4)-theory amplitudes can be continued to the half-plane. There are an infinite number of amplitudes whose natural domain of analyticity is given by this half-plane provided the Riemann conjecture about zeta -funct ion zeroes is valid.