and L-functions of elliptic curves. Computer calculations. (English) Zbl 0629.14002
Applications of algebraic K-theory to algebraic geometry and number theory, Proc. AMS-ISM-SIAM Joint Summer Res. Conf., Boulder/Colo. 1983, Part I, Contemp. Math. 55, 79-88 (1986).
[For the entire collection see Zbl 0588.00014.]
The paper concerns some computer calculations done by Grayson in the fall of 1981 to compare the value of the regulator on of an elliptic curve with the value of the L-function at . All curves on the Swinnerton-Dyer table [see “Modular functions of one Variable. IV” Proc. Internat. Summer School 1972, Univ. Antwerp, RUCA, Lect. Notes Math. 476 (1975; Zbl 0315.14014)] with Weil conductor , negative discriminant, and a rational torsion point of order were considered. These computations are explained by a modified form of a conjecture advanced by Bloch and Beilinson. They provide evidence for a lot of exotic relations between special values of Eisenstein-Kronecker- Lerch series and values of Hasse-Weil L-functions for elliptic curves without complex multiplication.
|14-04||Machine computation, programs (algebraic geometry)|
|14C35||Applications of methods of algebraic -theory|
|14G10||Zeta-functions and related questions|
|14H45||Special curves and curves of low genus|