For each k≥2 and s>2, the s-th moment of |∑_{n≤X} τ_k(n) e(nα)| is asymptotic to X^{s-1}(log X)^{s(k-1)} times an explicit series plus a power-saving error.
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Moment estimates for the exponential sum with higher divisor functions
For each k≥2 and s>2, the s-th moment of |∑_{n≤X} τ_k(n) e(nα)| is asymptotic to X^{s-1}(log X)^{s(k-1)} times an explicit series plus a power-saving error.