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# David Loeffler

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## Registered User

 Name David Loeffler Member for 3 years Seen yesterday Website Location University of Warwick Age 30
Number theorist working on p-adic automorphic forms
 Jun6 accepted PNT for number fields. Jun4 asked Modular symbols and degeneracy maps Jun3 comment Congruences between CM and non-CM modular formsVery nice answer -- thanks! Jun2 comment Congruences between CM and non-CM modular formsYes, (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. Jun2 revised Congruences between CM and non-CM modular formsadded requirement that ell is 1 mod p Jun2 revised Congruences between CM and non-CM modular formsquestion (1) was silly, edited it out Jun2 asked Congruences between CM and non-CM modular forms May14 comment References for period matrix of abelian varietyIt's still not clear why you expect there to be a meaningful definition of "period matrix" in this wider context. May12 comment Is there an algebraic curve over Q which is not modular?(Sorry, that should say $GSpin(2g + 1)$, of course.) May12 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 $GSp(4)$. May12 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. May12 awarded ● Nice Answer May11 answered Is there an algebraic curve over Q which is not modular? May10 comment the global m-th power reciprocity law and Quartic Reciprocity LawI fixed the formula. Sometimes putting backticks around formulae helps. May10 revised the global m-th power reciprocity law and Quartic Reciprocity Lawfixed formula May10 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". May10 awarded ● nt.number-theory May9 comment Elementary proof of algebraicity of Hecke eigenvalues in weight 1Of course! Very pretty. This one could certainly use in an undergrad course. May8 comment Concrete examples of noncongruence, arithmetic subgroups of SL(2,R)I added an explicit example for index 7. May8 revised Concrete examples of noncongruence, arithmetic subgroups of SL(2,R)Explicit $S_7$ example May8 revised Concrete examples of noncongruence, arithmetic subgroups of SL(2,R)Corrected a mistake about index 7 May8 awarded ● Nice Answer May8 comment Elementary proof of algebraicity of Hecke eigenvalues in weight 1I 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! May8 accepted Concrete examples of noncongruence, arithmetic subgroups of SL(2,R) May8 revised Concrete examples of noncongruence, arithmetic subgroups of SL(2,R)Improved formatting, corrected spelling, added subject-class tag May8 answered Concrete examples of noncongruence, arithmetic subgroups of SL(2,R) May7 awarded ● Nice Question May7 comment On the Cartan decomposition of unitary groupThe "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. May7 accepted On the Cartan decomposition of unitary group May6 answered On the Cartan decomposition of unitary group May3 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 May2 accepted j-invariant duplication, triplication and quintuplication formulae… how? May2 answered j-invariant duplication, triplication and quintuplication formulae… how? Apr27 comment Can we find a set of elliptic curves over rationals associated with $f$?.@RH: I don't understand, what exactly are you asking? Apr27 accepted Can we find a set of elliptic curves over rationals associated with $f$?. Apr27 answered Can we find a set of elliptic curves over rationals associated with $f$?. Apr24 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. Apr19 comment Integral conjugacy vs. Rational conjugacyWhat 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. Apr19 answered Sum of two random variables following K0 (modified 2nd kind Bessel) distributions Apr18 comment Slope of classical modular formsI 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. Apr18 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). Apr17 revised central/critical/special values of L-functions terminologyslightly less combative :-) Apr17 comment central/critical/special values of L-functions terminologyI 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. Apr17 answered central/critical/special values of L-functions terminology Apr16 awarded ● Good Answer Apr9 answered Lower bounds for Petersson inner products of cuspforms with integral Fourier coefficients Apr8 asked Twists of CM modular forms Mar27 comment About the boundedness of the set of Mordell-Weil ranksYou've told us what motivates your question and what your question is about, but you haven't actually asked a question. Mar22 awarded ● Popular Question Mar21 comment critical values of motivesI'm pretty sure that, the only integer $s$ such that $s \ge 2$ and $4-s \ge 2$ is $s = 2$.