ON P-ADIC ASPECTS OF SOME PERTURBATION-SERIES

Series with factorial terms, which are of potential interest in quantum field theory and string theory, are considered. Divergent series in the real case are usually p-adic convergent. Using simple and number field invariant methods of summation, rational sums are obtained. Sums of the convergent and divergent counterparts of the same series are connected by adelic summability.