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)[reply]

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)[reply]

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)[reply]

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)[reply]

Content Disclaimer

Informasi ini disarikan dari Wikipedia dan disajikan kembali untuk tujuan edukasi. Konten tersedia di bawah lisensi CC BY-SA 3.0. Kami tidak bertanggung jawab atas ketidakakuratan data yang bersumber dari kontribusi publik tersebut.

  1. The information displayed on this website is sourced in part or in whole from Wikipedia and has been adapted for the purpose of restating it. We strive to provide accurate and relevant information, however:
  2. There is no guarantee of absolute accuracy. Wikipedia is an open, collaborative project that can be edited by anyone, so information is subject to change.
  3. It is not intended to constitute professional advice. The content displayed is for informational and educational purposes only. For important decisions (e.g., medical, legal, or financial), please consult a professional.
  4. Content copyright. Wikipedia is licensed under the Creative Commons Attribution-ShareAlike License (CC BY-SA). This means that content may be reused with appropriate attribution and shared under a similar license.
  5. Responsible use. Any risk arising from the use of information from this website is entirely the responsibility of the user.