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Rational summation ofp-adic series

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Abstract

The problem of rational summation for a wide class ofp-adic convergent series is considered. Here, rational summation refers to the method of obtaining the rational sum of a power series for a rational value of its variable. A formula suitable for this summation is derived. Conditions for rational summability are obtained. Rational summation is possible only for special forms of the series. It is shown that the inverse problem of rational summation is always solvable. This is illustrated by some characteristic examples. Possible rational (adelic) summation of divergent perturbative expansions in string theory, and quantum field theory, is discussed.

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Authors
  1. B. G. Dragović
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Additional information

Institute of Physics, P.O. Box 57, 11001 Belgrade, Yugoslavia. Published in Toereticheskaya i Matematicheskaya Fizika, Vol. 100, No. 3, pp. 342–353, September, 1994.

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Dragović, B.G. Rational summation ofp-adic series. Theor Math Phys 100, 1055–1064 (1994). https://doi.org/10.1007/BF01018570

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  • DOI: https://doi.org/10.1007/BF01018570

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