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Apr
14
comment Algebra and Cancer Research
This is excellent!
Apr
14
comment Algebra and Cancer Research
This is exactly the sort of thing I'm looking for. Thank you!
Apr
14
comment Algebra and Cancer Research
@PerAlexandersson That sounds interesting. Can you give a reference for further reading? Thanks!
Feb
21
comment Elliptic curves over $\mathbb{Q}$ with no rational torsion and $\mu$-invariant equal to 1 at $p=3$
I see now...my mistake! Anyway, this would still be my suggested approach...
Feb
21
comment Elliptic curves over $\mathbb{Q}$ with no rational torsion and $\mu$-invariant equal to 1 at $p=3$
Pollack's table claims that $\mu=1$ at $p=3$.
Jan
9
comment Are the Fourier coefficients of a new form real
The reference for this is Proposition 3.2 of Ken Ribet's "Galois Representations Attached to Eigenforms with Nebentypus".
Jul
3
comment Hecke Characters
Ah, yes, those notes are dealing in a much more general setting (automorphic representations) than the one you care about (elliptic curves). Sorry about that. I don't have time to write something myself at the moment, and in any case, there are people here much more qualified than me to do so. I'm sorry that link wasn't more helpful!
Jul
3
comment Hecke Characters
You may find this resource helpful: www2.imperial.ac.uk/~tsg/Index_files/… In particular, see Theorem 2.41 on pg 12.
May
29
comment Examples of (Phi,Gamma)-modules
This doesn't really answer your question, but this paper of Laurent Berger is in the right direction: perso.ens-lyon.fr/laurent.berger/articles/article04.pdf
Jan
30
comment Research trends in geometry of numbers?
This is not new research in the geometry of numbers, but rather an application of classical results to another classical problem, that of determining primes of the form x^2+ny^2: tcnj.edu/~hagedorn/papers/…
Jan
24
comment Digital Copy of Kato's Paper
@YangMills That answers my question. Thank you very much!
Jan
24
comment Digital Copy of Kato's Paper
@Franz I'm not sure what you're implying with the "spamming" comment. I think this question is quite reasonable for MO, considering both the importance and scarcity of this paper. Scanning is not really an option since it is a borrowed book and I'm afraid that scanning would do considerable damage to the binding. @Serge Thanks, but I checked there and they don't have it. It's a hard paper to track down.
Jul
30
comment Number Fields Arising from Newforms
@Rob: Thank you! This is perfect.
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
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!
Oct
28
comment When are roots of power series algebraic?
Rob, this is wonderful...thank you!!
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
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?.