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International Algorithmic Number Theory Symposium

ANTS 2006: Algorithmic Number Theory pp 377–392Cite as

Symmetric Powers of Elliptic Curve L-Functions

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 4076))

Abstract

The conjectures of Deligne, Beĭlinson, 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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Authors and Affiliations

  1. University of Bristol,  

    Phil Martin & Mark Watkins

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  1. Phil Martin
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  2. Mark Watkins
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Editors and Affiliations

  1. Technische Universität Berlin, Germany

    Florian Hess

  2. Institut für Mathematik, MA 8–1, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Sebastian Pauli

  3. Institut für Mathematik, Technische Universität Berlin, Fakultät II, MA 8-1, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Michael Pohst

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Martin, P., Watkins, M. (2006). Symmetric Powers of Elliptic Curve L-Functions. In: Hess, F., Pauli, S., Pohst, M. (eds) Algorithmic Number Theory. ANTS 2006. Lecture Notes in Computer Science, vol 4076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11792086_27

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  • DOI: https://doi.org/10.1007/11792086_27

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  • Print ISBN: 978-3-540-36075-9

  • Online ISBN: 978-3-540-36076-6

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