An asymptotic estimate related to Selberg's sieve

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Abstract

Suppose 1 ≤ z1 ≤ z2 ≤ N, and let Λi(d) = μ(d) max(log( zi d), 0) for i = 1, 2. We show that ∑ N≤n ( ∑ d|nΛ1(d))( ∑ e|nΛ1(e)) = Nlog z1 + O(N). We then use this to improve a result of Barban-Vehov which has applications to zero-density theorems. © 1978.

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APA

Graham, S. (1978). An asymptotic estimate related to Selberg’s sieve. Journal of Number Theory, 10(1), 83–94. https://doi.org/10.1016/0022-314X(78)90010-0

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