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Jul
30
revised Number Fields Arising from Newforms
Paper was published in 1995, not 2007!
Jul
30
comment Number Fields Arising from Newforms
@Kevin Buzzard: Oh! You're absolutely right -- I see on Darmon's website that it was indeed published in 1995. I guess the tex file was recompiled in 2007, leading to the date I cited from this version of the paper: www.math.mcgill.ca/darmon/pub/Articles/Expository/05.DDT/paper.pdf Thanks!
Jul
30
awarded  Editor
Jul
30
revised Number Fields Arising from Newforms
Changed "modular form" to "normalized eigenform".
Jul
30
comment Number Fields Arising from Newforms
Hi Stopple, good point. It's a bad habit, but in my mind, when I say modular form I (almost) always mean "normalized eigenform", or even just "newform", but certainly the way I stated my question is incorrect. I'll fix my question to make it more precise. Thanks for pointing this out!
Jul
30
asked Number Fields Arising from Newforms
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?