Abstract
In this paper, we can show thatSΛ(x)=∑1≤n≤xΛ([xn])=∑n=1∞Λ(n)n(n+1)x+O(x7/15+1/195+ε), where Λ(n) is the von Mangdolt function. Moreover, we can also give similar results related to the divisor function, which improve previous results.
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