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Symmetric powers of elliptic curve L-functions

Research paper by Phil Martin, Mark Watkins

Indexed on: 17 Apr '06Published on: 17 Apr '06Published in: Mathematics - Number Theory



Abstract

The conjectures of Deligne, Be\u\i linson, 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.