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Jun
29
answered Computational number theory
Jun
28
answered Blackbox Theorems
Jun
26
awarded  Commentator
May
17
awarded  Popular Question
Dec
11
answered Suggestions for good books on class field theory
Oct
28
comment When are roots of power series algebraic?
Rob, this is wonderful...thank you!!
Oct
28
awarded  Nice Question
Oct
24
comment When are roots of power series algebraic?
@Lubin: This is a great (counter?)example. Thanks for this alternate perspective!
Oct
23
comment When are roots of power series algebraic?
@KConrad: Thank you, this is great!
Oct
23
accepted When are roots of power series algebraic?
Oct
23
comment When are roots of power series algebraic?
@Robert: Thank you for explaining that with such a simple, succinct argument!
Oct
22
comment When are roots of power series algebraic?
@David: I'm not sure I understand. In the example quoted in my question (the middle paragraph), a priori $f$ does not have coefficients in the ring of integers of $K$. The only thing known about $f$ is that it is a formal power series with coefficients in $K$ which converges in the open unit disc of $\mathbb{C}_p$ and has finitely many zeros. Where (and how) is the Weierstrass Preparation Theorem being invoked here?.
Oct
21
comment When are roots of power series algebraic?
@Qiaochu: Yes, Jacques has the right idea. @KConrad: Yes, the Weierstrass Preparation Theorem is a great example of this phenomenon. Thank you.
Oct
21
asked When are roots of power series algebraic?
Sep
15
awarded  Scholar
Sep
15
accepted Prime Decomposition in Cyclotomic Z_p-extensions
Sep
15
awarded  Student
Sep
15
asked Prime Decomposition in Cyclotomic Z_p-extensions
Jul
14
awarded  Supporter
Jul
12
comment Changing field of study post-PhD
@quid: I was thinking the exact same thing when I wrote this answer! And no disrespect taken: I am certainly not one of those people! It is definitely easier for some people to transition between fields, but I suppose the existence of any such people at all should be encouraging to people like Adam.