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Zbl 0629.14002
Bloch, S.; Grayson, D.
$K\sb 2$ and L-functions of elliptic curves. Computer calculations. (English)
[A] 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.] \par The paper concerns some computer calculations done by Grayson in the fall of 1981 to compare the value of the regulator on $K\sb 2$ of an elliptic curve with the value of the L-function at $s=2$. 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 $\le 180$, negative discriminant, and a rational torsion point of order $\ge 5$ 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.
[Ş.A.Basarab]

MSC 2000:: *14-04 Machine computation, programs (algebraic geometry)
14C35 Appl. of methods of algebraic K-theory
14G10 Zeta-functions and related questions
14H45 Special curves and curves of low genus
14H52 Elliptic curves

Keywords: regulator; elliptic curve; L-function; Eisenstein-Kronecker-Lerch series

Citations: Zbl 0588.00014; Zbl 0315.14014

Cited in: Zbl 1174.11049 Zbl 1163.11045 Zbl 1048.11081 Zbl 0782.14023

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