Symmetric Powers of Elliptic Curve L-Functions

Abstract. The conjectures of Deligne, Beilinson, and Bloch-Kato assert that there should be relations between the arithmetic of algebrogeometric objects and the special values of their L-functions. We make a numerical study for symmetric power L-functions of elliptic curves, obtaining data about the validity of their functional equations, frequency of vanishing of central values, and divisibility of Bloch-Kato quotients.

• Type: Conference
• Year: 2006
• Where: ANTS
• Authors: Phil Martin, Mark Watkins
• Keywords: Algorithms, ANTS 2006, Bloch-Kato Assert, Special Values, Symmetric Power L-functions