On relations between Jacobians of certain modular curves
| dc.creator | Chen, Imin | |
| dc.date | 1998-09-03 | |
| dc.date.accessioned | 2026-07-07T05:26:15Z | |
| dc.date.available | 2026-07-07T05:26:15Z | |
| dc.description | The topic of this paper concerns a certain relation between the jacobians of various quotients of the modular curve $X(p)$, which relates the jacobian of the quotient of $X(p)$ by the normaliser of a non-split Cartan subgroup of $GL_2(F_p)$ to the jacobians of more standard modular curves. In this paper, we confirm a conjecture of Merel found in a paper of Darmon-Merel, "Winding quotients and some variants of Fermat's Last Theorem", Crelle, v. 490, p. 81-100, 1997, which describes this relation in terms of explicit correspondences. The method used is to reduce the conjecture to showing a certain $Z[GL_2(F_p)]$-module homomorphism is an isomorphism. This is accomplished by using some peculiar relations between double coset operators to find a expression for the eigenvalues of this homomorphism in terms of Legendre character sums and Soto-Andrade sums. A ramification argument then shows that these eigenvalues are non-zero. | |
| dc.identifier | https://arxiv.org/abs/math/9809209 | |
| dc.identifier | http://arxiv.org/abs/math/9809209 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77482 | |
| dc.subject | Number Theory | |
| dc.title | On relations between Jacobians of certain modular curves | |
| dc.type | text |