Talk:Mahler's theorem

"It is a fact of algebra that if f is a polynomial function with coefficients in any specified field, the same identity holds."

Did you mean to say "in any field of characteristic 0"? For characteristic p>0, I'm not sure what the formula would mean.

Crust 18:40, 24 Mar 2005 (UTC)

continuous with respect to which topology?
The article needs a link to the article that defines p-adic continuity. I presume is the standard cylinder set/ p-adic's as a metric space topology, but being precise would be nice. linas 00:47, 15 February 2006 (UTC)

why compare w. the real numbers?
the comparison with the situation for real numbers is a bit weird to me, since the theorem talks about continuous functions on the p-adic integers, not the p-adic numbers which would be in closer analogy to the reals. but I'm no expert :) —Preceding unsigned comment added by 83.183.186.185 (talk) 09:28, 26 April 2009 (UTC)

Interpretation
So you can use merely continuous functions over the p-adic numbers but requires derivatives over the reals. What does that mean? Crasshopper (talk) 10:12, 19 December 2010 (UTC)

Self-contradictory on continuity
The article at states that f being a polynomial can't be weakened down to continuity, but remarkably it can. Finite difference states, "In analysis with p-adic numbers, Mahler's theorem states that the assumption that f is a polynomial function can be weakened all the way to the assumption that f is merely continuous." The statement that it can't needs to be qualified, so that it shows what the barrier to weakening was, and of course for the development of the article, how it's circumvented. ᛭ LokiClock (talk) 06:43, 22 January 2012 (UTC)