Density of rational points on diagonal quartic surfaces

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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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Algebraic Geometry, Number Theory, 11Dxx, 11Gxx, 14Gxx, 14Jxx

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http://salesiana.dossiersoluciones.com/handle/123456789/221578

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0812.4779
 http://arxiv.org/abs/0812.4779

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arXiv