Density of rational points on diagonal quartic surfaces
Algebraic Geometry
2009-02-27 v3 Number Theory
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.
Cite
@article{arxiv.0812.4779,
title = {Density of rational points on diagonal quartic surfaces},
author = {Adam Logan and David McKinnon and Ronald van Luijk},
journal= {arXiv preprint arXiv:0812.4779},
year = {2009}
}
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