# Density of rational points on diagonal quartic surfaces

```@article{Logan2008DensityOR,
title={Density of rational points on diagonal quartic surfaces},
author={Adam Logan and David McKinnon and Ronald van Luijk},
journal={arXiv: Algebraic Geometry},
year={2008}
}```
• Published 27 December 2008
• Mathematics
• arXiv: Algebraic Geometry
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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