All Questions
8 questions
10
votes
2
answers
404
views
Impact of the squarefreeness of the level for modular forms
I often notice papers and results that assume that the level is squarefree in the setting of modular forms, but have a hard time figuring how where this impacts or simplifies the argument. Is there in ...
- 23k
23
votes
2
answers
3k
views
How can I see the relation between shtukas and the Langlands conjecture?
The following bullet points represent the very peak of my understanding of the resolution of the Langlands program for function fields. Disclaimer: I don't know what I'm writing about.
Drinfeld ...
CommunityBot
- 1
3
votes
1
answer
243
views
Does weight $2$ cuspidal Bianchi modular form have infinitely many zero Fourier coefficient at prime ideals?
Let $K$ be an imaginary quadratic field. Let $f \in S_2(\mathfrak{n})$ be a weight $2$ cuspidal cof level $\Gamma_0(\mathfrak{n})$ over $K$ (for definitions one can see http://www.lmfdb.org/knowledge/...
- 6,622
4
votes
1
answer
383
views
Is there a characterization of the cuspidal automorphic representations that arise from elliptic curves?
Is there a way to characterize (e.g. by their local components) the cuspidal automorphic representations that arise from elliptic curves? There is a procedure to go from elliptic curves to cuspidal ...
- 3,058
7
votes
1
answer
317
views
When is the local representation associated to an elliptic curve a Steinberg?
If $E$ is an elliptic curve over $\mathbb{Q}$, and $\pi$ is the automorphic representation of $\mathrm{GL}_2$ associated to $E$, then one can write $\pi = \otimes_v \pi_v$ with each $\pi_v$ an ...
- 20.4k
13
votes
2
answers
781
views
Elliptic curves and supercuspidal representations of conductor $p^2$
Let $E$ be an elliptic curve defined over $\mathbf{Q}$. Let $p \geq 5$ be a prime of additive reduction for $E$.
Let $f$ be the newform associated to $E$, and let $\pi$ be the irreducible admissible ...
- 148k
13
votes
0
answers
2k
views
Why doesn't functoriality immediately imply the modularity theorem?
Let $E/\mathbb{Q}$ be an elliptic curve. By the modularity theorem, the prime indexed coefficients of its $L$-function agree with those of a weight $2$ cusp eigenform $f$ with integer coefficients. ...
- 7,062
5
votes
1
answer
630
views
Special value of $L$-function
Let $p$ be a prime number. Let $f$ be a newform of weight 2 on $Γ_0(p)$, and $E_f$ denote the associated newform quotient of $J_0 (N)$ over $\mathbb{Q}$. Is there a way to express the
algebraic part ...
- 23k