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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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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