Improved asymptotic for T(x) = ∑_{n≤x} τ([x/n]) τ(n) with error O(x^{17/30+ε}), obtained via new bounds on three-dimensional exponential sums with constant perturbation.
Zhang,On a variant of the prime number theorem, J
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On the Hyperbolic Fractional Sum of the Divisor Function
Improved asymptotic for T(x) = ∑_{n≤x} τ([x/n]) τ(n) with error O(x^{17/30+ε}), obtained via new bounds on three-dimensional exponential sums with constant perturbation.