Systems of odd-degree forms in s variables (s large depending on R and d) have at least C N^{s-D} / (log N)^s almost-prime solutions in large boxes.
The density of integral points on complete intersections.The Quarterly Journal of Mathematics, 59(1):29–53, 2008
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On almost primes solutions to forms of odd degrees in many variables
Systems of odd-degree forms in s variables (s large depending on R and d) have at least C N^{s-D} / (log N)^s almost-prime solutions in large boxes.