On Bombieri's asymptotic sieve

Details On Bombieri's asymptotic sieve On Bombieri's asymptotic sieve

2004-01-18

arxiv.org/abs/math/0401215v1

Trans. Amer. Math. Soc. 357 (2005), 1663-1674.

Mathematics

Number Theory

13 pages. To appear in Trans. Amer. Math. Soc. http://www.math.uiuc.edu/~ford/

Scientific paper

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 $\sum_{n\le x} a_n \Lambda_k(n)$ 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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