Let be a complete non-Archimedean Valuated Field, with Valuation Ring , and let be a Power series with Coefficients in . Suppose at least one of the Coefficients is Nonzero (so that is not identically zero) and the sequence of Coefficients converges to 0 with respect to . Then has only finitely many zeros in .
See also Archimedean Valuation, Mahler-Lech Theorem, Valuation, Valuation Ring