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On Bombieri's asymptotic sieve

Kevin Ford
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Abstract

If a sequence $(a_n)$ of non-negative real numbers has ``best possible'' distribution in arithmetic progressions, Bombieri showed that one can deduce an asymptotic formula for the sum $\sum_{n\le x} a_n Λ_k(n)$ for $k\ge 2$. By constructing appropriate sequences, we show that any weakening of the well-distribution property is not sufficient to deduce the same conclusion.

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Kevin Ford. 2004-01-18. On Bombieri's asymptotic sieve. https://arxiv.org/abs/math/0401215

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