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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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On the factor alpha in Peyre’s constant
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by Ulrich Derenthal, Andreas-Stephan Elsenhans and Jörg Jahnel PDF
Math. Comp. 83 (2014), 965-977


For an arbitrary del Pezzo surface $S$, we compute $\alpha (S)$, which is the volume of a certain polytope in the dual of the effective cone of $S$, using magma and polymake. The constant $\alpha (S)$ appears in Peyre’s conjecture for the asymptotic formula for the number of rational points of bounded height on $S$ over number fields.
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Additional Information
  • Ulrich Derenthal
  • Affiliation: Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresienstr. 39, D-80333 München, Germany
  • MR Author ID: 776744
  • Email:
  • Andreas-Stephan Elsenhans
  • Affiliation: School of Mathematics and Statistics F07, University of Sydney, NSW 2006, Sydney, Australia
  • Email:
  • Jörg Jahnel
  • Affiliation: Département Mathematik, Universität Siegen, Walter-Flex-Str. 3, D-57068 Siegen, Germany
  • Email:
  • Received by editor(s): February 28, 2012
  • Published electronically: September 17, 2013
  • Additional Notes: The first author was partly supported by Deutsche Forschungsgemeinschaft (DFG) grant DE 1646/2-1, SNF grant 200021_124737/1, and by the Center for Advanced Studies of LMU München.
    The second author was supported in part by the Deutsche Forschungsgemeinschaft (DFG) through a funded research project.
  • © Copyright 2013 by U. Derenthal, A.-S. Elsenhans, and J. Jahnel
  • Journal: Math. Comp. 83 (2014), 965-977
  • MSC (2010): Primary 14J26; Secondary 51M20, 14G05
  • DOI:
  • MathSciNet review: 3143700