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Results tagged with hecke-operators
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user 394740
1
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1
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293
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What is the image of the Hecke operator $U_p$?
Let $N \geq 1$ be an integer and let $p$ be a prime not dividing $N$. For $r \geq 1$, let $M_2(\Gamma_0(Np^r))$ denote the space of weight $2$ modular forms of level $\Gamma_0(Np^r)$. Let $$U_p: M_2(\ …
- 1,949
3
votes
1
answer
300
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Hecke operators on universal elliptic curves
Suppose that $\tau \in \mathbf{H}$ belongs to the complex upper half plane. The quotient $\mathbf{C}/(\mathbf{Z}+\mathbf{Z}\tau)$ gives an elliptic curve over $\mathbf{C}$. Write this elliptic curve a …
- 1,949
2
votes
0
answers
289
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Hecke operators acting on the Weierstrass $\wp$-function
Roughly speaking, my question is the following: Let $\wp(\tau, z)$ be the Weierstrass $\wp$-function, where $\tau \in \mathbf{H}$ and $z \in \mathbf{C}$. If $p$ is a prime number, can we define $T_p\, …
- 1,949