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Tagged with modular-group elliptic-curves
5 questions
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GL2 action on torsion sections of elliptic curves
I am reading Kato's $p$-adic Hodge theory paper and I am confused about a rather embarrassing and admittedly very minor thing, but it is nevertheless important.
In Section 1.6 of Kato, it is claimed ...
- 751
1
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1
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61
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Meaning of this Eisenstein series notation from Gross–Zagier paper [duplicate]
In equation (2.14) of their paper [1], Gross–Zagier define the following Eisenstein series
\begin{align}
E_N(z, s) = \sum_{\gamma \in \bigg(\begin{matrix} \ast & \ast \\ 0 & \ast \end{matrix}\...
- 404
1
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238
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Isomorphism of lattices/complex tori
This is essentially a reference request (apologies if it is a duplicate): it is known that every lattice $\Lambda$ in $\mathbb{C}$ is isomorphic to one of the form $\mathbb{Z} \oplus \mathbb{Z}[\tau]$ ...
- 404
0
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0
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128
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why is $\Gamma(1)\setminus H$ a 2-sphere with one point missing?
I am reading Silverman's book about elliptic curves.
$\Gamma(1):=SL_{2}(\mathbb{Z})/\{\pm 1\}$ is the modular group, and $H$ is the upper half plane. The author says that the geometric description ...
- 1,957
2
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To prove that the Elliptic modular function is invariant under the modular transformation
I am not being able to understand that the Elliptic modular function $J(\tau)=\frac{g_2(w_1,w_2)^3}{g_2(w_1,w_2)^3-27g_3(w_1,w_2)^2}$ is invariant under the modular transformation $\tau\mapsto \frac{a\...
- 1,449