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The Asymptotics of Points of Bounded Height on Diagonal Cubic and Quartic Threefolds

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Algorithmic Number Theory (ANTS 2006)

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

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Abstract

For the families ax 3 = by 3 + z 3 + v 3 + w 3, a, b = 1, ... ,100, and ax 4 = by 4 + z 4 + v 4 + w 4, a, b = 1, ... ,100, of projective algebraic threefolds, we test numerically the conjecture of Manin (in the refined form due to Peyre) about the asymptotics of points of bounded height on Fano varieties.

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Author information

Authors and Affiliations

  1. Mathematisches Institut, Universität Göttingen, Bunsenstraße 3–5, D-37073, Göttingen, Germany

    Andreas-Stephan Elsenhans & Jörg Jahnel

Authors
  1. Andreas-Stephan Elsenhans
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  2. Jörg Jahnel
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Editor information

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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Elsenhans, AS., Jahnel, J. (2006). The Asymptotics of Points of Bounded Height on Diagonal Cubic and Quartic Threefolds. 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_23

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  • DOI: https://doi.org/10.1007/11792086_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-36075-9

  • Online ISBN: 978-3-540-36076-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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