Remote Access Mathematics of Computation
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 11Y50, 14G05, 14J28

Retrieve articles in all journals with MSC (2010): 11Y50, 14G05, 14J28

Additional Information

Andreas-Stephan Elsenhans
Affiliation: Mathematisches Institut, Universität Bayreuth, Universitätsstraße 30, D-95440 Bayreuth, Germany

Keywords: $\mathrm {K3}$ 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.