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.
On forms in prime variables.Transactions of the American Mathematical Society, 376(12):8621–8656
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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.