Symmetric powers of elliptic curve L-functions

Phil Martin; Mark Watkins

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Symmetric powers of elliptic curve L-functions

Phil Martin·Mark Watkins

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Abstract

The conjectures of Deligne, Be\uılinson, 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.

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Phil Martin, Mark Watkins. 2006-04-17. Symmetric powers of elliptic curve L-functions. https://arxiv.org/abs/math/0604095

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