bio | website | |
---|---|---|
location | ||
age | ||
visits | member for | 3 years, 11 months |
seen | 20 hours ago | |
stats | profile views | 287 |
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. |