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2010 Density of rational points on diagonal quartic surfaces
Adam Logan, David McKinnon, Ronald van Luijk
Algebra Number Theory 4(1): 1-20 (2010). DOI: 10.2140/ant.2010.4.1

Abstract

Let a,b,c,d be nonzero rational numbers whose product is a square, and let V be the diagonal quartic surface in 3 defined by ax4+by4+cz4+dw4=0. We prove that if V contains a rational point that does not lie on any of the 48 lines on V or on any of the coordinate planes, then the set of rational points on V is dense in both the Zariski topology and the real analytic topology.

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Adam Logan. David McKinnon. Ronald van Luijk. "Density of rational points on diagonal quartic surfaces." Algebra Number Theory 4 (1) 1 - 20, 2010. https://doi.org/10.2140/ant.2010.4.1

Information

Received: 27 December 2008; Revised: 29 July 2009; Accepted: 9 November 2009; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1206.11082
MathSciNet: MR2592011
Digital Object Identifier: 10.2140/ant.2010.4.1

Subjects:
Primary: 11D25
Secondary: 14G05 , 14J28

Keywords: elliptic surfaces , K3 surfaces , quartic surfaces , rational points

Rights: Copyright © 2010 Mathematical Sciences Publishers

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