For an open subgroup $H \leq \GL_2(\widehat \Z)$, the Gassmann class of $H$ is the set of open subgroups of $\GL_2(\widehat \Z)$ that are Gassmann equivalent to $H$.
Let $H,H' \leq \GL_2(\widehat \Z)$ be in the same Gassmann class. Then $H,H'$ have the same level, index and genus. Moreover, the Jacobians of $X_H$ and $X_{H'}$ are isogenous (see Corollary 4 of Prasad-Rajan [10.1016/S0022-314X(02)00053-7], applied to the covering curve $X_{\mathrm{full}}(N)$), hence $L(X_H,s)=L(X_{H'},s)$.
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- Last edited by Andrew Sutherland on 2024-03-16 11:04:01
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- 2024-03-16 11:04:01 by Andrew Sutherland (Reviewed)
- 2024-03-15 13:40:35 by John Voight
- 2024-03-15 13:40:26 by John Voight
- 2024-03-15 12:18:34 by John Voight (Reviewed)
- 2024-03-15 12:16:04 by John Voight (Reviewed)
- 2024-03-15 12:14:30 by John Voight
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- 2024-03-15 12:09:55 by John Voight
- 2024-03-15 08:25:19 by Andrew Sutherland
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- 2024-03-14 21:24:19 by Andrew Sutherland
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- 2024-03-14 21:12:56 by Andrew Sutherland
- 2023-01-03 11:41:58 by Andrew Sutherland