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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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Rational points on diagonal quartic surfaces
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by Andreas-Stephan Elsenhans PDF
Math. Comp. 81 (2012), 481-492 Request permission

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.
References
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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
  • 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.
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 81 (2012), 481-492
  • MSC (2010): Primary 11Y50; Secondary 14G05, 14J28
  • DOI: https://doi.org/10.1090/S0025-5718-2011-02500-7
  • MathSciNet review: 2833505