Forms in many variables
- 23 January 1962
- journal article
- Published by The Royal Society in Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- Vol. 265 (1321) , 245-263
- https://doi.org/10.1098/rspa.1962.0007
Abstract
It is proved that iffis a homogeneous form of degreedwith rational coefficients then the variety V:f= 0 certainly has rational points if it has non-singular real points and nonsingularp-adic points for everyp, and if its singular locus has codimension sufficiently large compared with the degreed. The methods used are derived from those of Davenport (1959); considerable generalizations are made, and geometric conditions have to be introduced. The discussion of the singular integral presents unexpected difficulty.Keywords
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