Let K be a number field, and let X ⊆ ℙs-1K be a smooth complete intersection defined over K. In this paper, weak approximation is shown to hold for X provided s exceeds some function of the degree and codimension of X. This is a corollary of a more general result about the number of integral points on certain affine varieties in homogeneously expanding regions. This general result is established via a suitable adaptation of the Hardy-Littlewood Circle Method.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Forms in many variables
- Hardy-Littlewood method
- Weak approximation