Density of rational points on diagonal quartic surfaces
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.
 Publication:

arXiv eprints
 Pub Date:
 December 2008
 arXiv:
 arXiv:0812.4779
 Bibcode:
 2008arXiv0812.4779L
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Number Theory;
 11Dxx;
 11Gxx;
 14Gxx;
 14Jxx
 EPrint:
 added reference