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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