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David Loeffler

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Name David Loeffler
Member for 3 years
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Location University of Warwick
Age 30
Number theorist working on p-adic automorphic forms
Jun
6
 accepted PNT for number fields.
Jun
4
 asked Modular symbols and degeneracy maps
Jun
3
 comment Congruences between CM and non-CM modular forms
Very nice answer -- thanks!
Jun
2
 comment Congruences between CM and non-CM modular forms
Yes, (1) was a silly question, sorry! For (2), I did do some computer checks, and your question prompted me to make some more; at the second attempt I found an example with g the CM form of level 32, N = 17, and p = 5, but in fact for the special case I have in mind it would suffice to consider ell such that ell = 1 mod p, and I didn't find any examples where this is the case.
Jun
2
 revised Congruences between CM and non-CM modular forms
added requirement that ell is 1 mod p
Jun
2
 revised Congruences between CM and non-CM modular forms
question (1) was silly, edited it out
Jun
2
 asked Congruences between CM and non-CM modular forms
May
14
 comment References for period matrix of abelian variety
It's still not clear why you expect there to be a meaningful definition of "period matrix" in this wider context.
May
12
 comment Is there an algebraic curve over Q which is not modular?
(Sorry, that should say $GSpin(2g + 1)$, of course.)
May
12
 comment Is there an algebraic curve over Q which is not modular?
@Keerthi: it is true that irreducible 2g-dimensional symplectic Galois representations should correspond to automorphic forms on $GSpin(2n+1)$, but there is an exceptional isomorphism between $GSpin(5)$ and $GSp(4)$.
May
12
 comment Is there an algebraic curve over Q which is not modular?
The H^1 is (up to twist) the Tate module of the Jacobian, and the representation on the Tate module of the Jacobian has to preserve the Weil pairing into roots of unity, which is a symplectic pairing.
May
12
 awarded ● Nice Answer
May
11
 answered Is there an algebraic curve over Q which is not modular?
May
10
 comment the global m-th power reciprocity law and Quartic Reciprocity Law
I fixed the formula. Sometimes putting backticks around formulae helps.
May
10
 revised the global m-th power reciprocity law and Quartic Reciprocity Law
fixed formula
May
10
 comment Concrete examples of noncongruence, arithmetic subgroups of SL(2,R)
I am no expert here, but I thought the CSP was still open for lots of real rank 1 groups. I guess it all depends wht kind of groups you consider "natural".
May
10
 awarded ● nt.number-theory
May
9
 comment Elementary proof of algebraicity of Hecke eigenvalues in weight 1
Of course! Very pretty. This one could certainly use in an undergrad course.
May
8
 comment Concrete examples of noncongruence, arithmetic subgroups of SL(2,R)
I added an explicit example for index 7.
May
8
 revised Concrete examples of noncongruence, arithmetic subgroups of SL(2,R)
Explicit $S_7$ example
May
8
 revised Concrete examples of noncongruence, arithmetic subgroups of SL(2,R)
Corrected a mistake about index 7
May
8
 awarded ● Nice Answer
May
8
 comment Elementary proof of algebraicity of Hecke eigenvalues in weight 1
I think filling in all the steps here is actually quite a lot harder than the argument I mentioned above. Nonetheless, if you assume Deligne--Serre it's certainly a nice short argument!
May
8
 accepted Concrete examples of noncongruence, arithmetic subgroups of SL(2,R)
May
8
 revised Concrete examples of noncongruence, arithmetic subgroups of SL(2,R)
Improved formatting, corrected spelling, added subject-class tag
May
8
 answered Concrete examples of noncongruence, arithmetic subgroups of SL(2,R)
May
7
 awarded ● Nice Question
May
7
 comment On the Cartan decomposition of unitary group
The "exact form of K" depends rather on whether $F$ is archimedean or nonarchimedean. For $F = \mathbb{R}$, you can use the fact that the indefinite special unitary group in 2 variables, $SU(1,1)$, is isomorphic to $SL(2)$ and the max compact subgroup of the latter is well known.
May
7
 accepted On the Cartan decomposition of unitary group
May
6
 answered On the Cartan decomposition of unitary group
May
3
 comment j-invariant duplication, triplication and quintuplication formulae… how?
You probably want to read a book on modular forms; but modern books on this subject (Diamond+Shurman is the standard one) tend to avoid stressing these sorts of explicit special-functions aspects in favour of more abstract treatments based on Riemann surfaces. You could perhaps try the section on modular forms + modular functions in Knapp's book on elliptic curves, or McKean + Moll's book on elliptic functions + elliptic curves
May
2
 accepted j-invariant duplication, triplication and quintuplication formulae… how?
May
2
 answered j-invariant duplication, triplication and quintuplication formulae… how?
Apr
27
 comment Can we find a set of elliptic curves over rationals associated with $f$?.
@RH: I don't understand, what exactly are you asking?
Apr
27
 accepted Can we find a set of elliptic curves over rationals associated with $f$?.
Apr
27
 answered Can we find a set of elliptic curves over rationals associated with $f$?.
Apr
24
 comment reference request for the finiteness of cuspidal subgroup of $X_0(N)$?
The statement is one about all cusps (not necessarily $\mathbb{Q}$-rational ones). The original paper by Drinfeld, "Two theorems on modular curves", is very readable.
Apr
19
 comment Integral conjugacy vs. Rational conjugacy
What group would be acting here? Whether or not two $G(F)$-conjugate elements are $G(\mathcal{O})$-conjugate is nothing to do with the Galois action, so it doesn't seem reasonable to expect that you can measure it with a Galois cohomology group.
Apr
19
 answered Sum of two random variables following K0 (modified 2nd kind Bessel) distributions
Apr
18
 comment Slope of classical modular forms
I suspect that by "Kevin Buzzard's second paper on the Artin conjecture", Joël means the 2003 JAMS paper /Analytic continuation of overconvergent eigenforms/ (www2.imperial.ac.uk/~buzzard/maths/research/…). The goal of this paper is to prove cases of Artin's conjecture, but the paper's title describes the method rather than the goal.
Apr
18
 comment central/critical/special values of L-functions terminology
@Matt: I've never seen the terminology you mention, and would consider it bizarre and confusing (particularly in even motivic weight).
Apr
17
 revised central/critical/special values of L-functions terminology
slightly less combative :-)
Apr
17
 comment central/critical/special values of L-functions terminology
I see what you mean, but the normalization is inconvenient when the $L$-function really is motivic and you are interested in special values, which was the context of the question.
Apr
17
 answered central/critical/special values of L-functions terminology
Apr
16
 awarded ● Good Answer
Apr
9
 answered Lower bounds for Petersson inner products of cuspforms with integral Fourier coefficients
Apr
8
 asked Twists of CM modular forms
Mar
27
 comment About the boundedness of the set of Mordell-Weil ranks
You've told us what motivates your question and what your question is about, but you haven't actually asked a question.
Mar
22
 awarded ● Popular Question
Mar
21
 comment critical values of motives
I'm pretty sure that, the only integer $s$ such that $s \ge 2$ and $4-s \ge 2$ is $s = 2$.