Parabolic points and zeta-functions of modular curves
Izvestiya. Mathematics , Tome 6 (1972) no. 1, pp. 19-64
Voir la notice de l'article provenant de la source Math-Net.Ru
In this paper we obtain explicit formulas for the values at the center of the critical strip of Dirichlet series connected with weight 2 parabolic forms of the group $\Gamma_0(N)$. In particular, these formulas allow us to verify the Birch–Swinnerton-Dyer conjecture on the order of a zero for uniformizable elliptic curves over certain $\Gamma$-extensions. We also give applications to noncommutative reciprocity laws.
@article{IM2_1972_6_1_a1,
author = {Yu. I. Manin},
title = {Parabolic points and zeta-functions of modular curves},
journal = {Izvestiya. Mathematics },
pages = {19--64},
publisher = {mathdoc},
volume = {6},
number = {1},
year = {1972},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_1972_6_1_a1/}
}
Yu. I. Manin. Parabolic points and zeta-functions of modular curves. Izvestiya. Mathematics , Tome 6 (1972) no. 1, pp. 19-64. http://geodesic.mathdoc.fr/item/IM2_1972_6_1_a1/