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arXiv · 0812.4779

Density of rational points on diagonal quartic surfaces

Adam Logan·David McKinnon·Ronald van Luijk
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Abstract

Let a,b,c,d be nonzero rational numbers whose product is a square, and let V be the diagonal quartic surface in PP^3 defined by ax^4+by^4+cz^4+dw^4=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. 2009-02-27. Density of rational points on diagonal quartic surfaces. https://arxiv.org/abs/0812.4779

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