Strassman's theorem states that a nonzero power series over a complete non-Archimedean valued field whose coefficients
tend to zero has only finitely many zeros in its valuation
ring. 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 
.
Strassman's Theorem
See also
Archimedean Valuation, Mahler-Lech Theorem, Valuation, Valuation RingExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Strassman's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StrassmansTheorem.html