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- W1660812153 abstract "We study the special value at 2 of L-functions of modular forms of weight 2 on congruence subgroups of the modular group. We prove an explicit version of Beilinson's theorem for the modular curve X_1(N). When N is prime, we deduce that the target space of Beilinson's regulator map is generated by the images of Milnor symbols associated to modular units of X_1(N). We also suggest a reformulation of Zagier's conjecture on L(E,2) for the jacobian J_1(N) of X_1(N), where E is an elliptic curve of conductor N. In this direction we define an analogue of the elliptic dilogarithm for any jacobian J : it is a function R_J from the complex points of J to a finite-dimensional vector space. In the case J=J_1(N), we establish a link between the aforementioned L-values and the function R_J evaluated at Q-rational points of the cuspidal subgroup of J." @default.
- W1660812153 created "2016-06-24" @default.
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- W1660812153 date "2006-02-09" @default.
- W1660812153 modified "2023-09-27" @default.
- W1660812153 title "Value at 2 of the L-function of an elliptic curve" @default.
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