Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

   
 

 

On the factor alpha in Peyre's constant


Authors: Ulrich Derenthal, Andreas-Stephan Elsenhans and Jörg Jahnel
Journal: Math. Comp. 83 (2014), 965-977
MSC (2010): Primary 14J26; Secondary 51M20, 14G05
Published electronically: September 17, 2013
MathSciNet review: 3143700
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: 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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 14J26, 51M20, 14G05

Retrieve articles in all journals with MSC (2010): 14J26, 51M20, 14G05


Additional Information

Ulrich Derenthal
Affiliation: Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresienstr.39, D-80333 München, Germany
Email: ulrich.derenthal@mathematik.uni-muenchen.de

Andreas-Stephan Elsenhans
Affiliation: School of Mathematics and Statistics F07, University of Sydney, NSW 2006, Sydney, Australia
Email: stephan@maths.usyd.edu.au

Jörg Jahnel
Affiliation: Département Mathematik, Universität Siegen, Walter-Flex-Str. 3, D-57068 Siegen, Germany
Email: jahnel@mathematik.uni-siegen.de

DOI: https://doi.org/10.1090/S0025-5718-2013-02772-X
Keywords: Peyre's constant, del Pezzo surface, polyhedron, volume, polymake
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.
Article copyright: © Copyright 2013 by U. Derenthal, A.-S. Elsenhans, and J. Jahnel