New mean value estimates for exponential sums over y-smooth numbers with y=(log x)^{K+o(1)} give a power saving over the trivial bound in an intermediate range, and yield a nontrivial bound on additive energy for K>12.
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Mean value theorems with smooth numbers
New mean value estimates for exponential sums over y-smooth numbers with y=(log x)^{K+o(1)} give a power saving over the trivial bound in an intermediate range, and yield a nontrivial bound on additive energy for K>12.