The conjectures of Deligne, Beuilinson, and Bloch-Kato assert that there should be relations between the arithmetic of algebro-geometric 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.
Martin, Phil and Watkins, Mark, "Symmetric Powers of Elliptic Curve L-Functions" (2006). Mathematics Faculty Scholarship. Paper 109.
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