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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Rational points on diagonal quartic surfaces


Author: Andreas-Stephan Elsenhans
Journal: Math. Comp. 81 (2012), 481-492
MSC (2010): Primary 11Y50; Secondary 14G05, 14J28
Published electronically: May 12, 2011
MathSciNet review: 2833505
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Abstract: We searched up to height $ 10^7$ for rational points on diagonal quartic surfaces. The computations fill several gaps in earlier lists computed by Pinch, Swinnerton-Dyer, and Bright.


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Additional Information

Andreas-Stephan Elsenhans
Affiliation: Mathematisches Institut, Universität Bayreuth, Universitätsstraße 30, D-95440 Bayreuth, Germany
Email: Stephan.Elsenhans@uni-bayreuth.de

DOI: http://dx.doi.org/10.1090/S0025-5718-2011-02500-7
PII: S 0025-5718(2011)02500-7
Keywords: K3 surface, diagonal quartic surface, rational point, Diophantine equation, computer solution, hashing
Received by editor(s): August 19, 2010
Received by editor(s) in revised form: October 13, 2010, and November 2, 2010
Published electronically: May 12, 2011
Additional Notes: The author was supported by the Deutsche Forschungsgemeinschaft (DFG)
The computer part of this work was executed on the servers of the chair for Computer Algebra at the University of Bayreuth. The author is grateful to Professor M. Stoll for permission to use these machines. He is also grateful to the system administrators for their support.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.