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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? |