On Bombieri's asymptotic sieve

Kevin Ford

On Bombieri's asymptotic sieve

Number Theory 2007-05-23 v1

Authors: Kevin Ford

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

Keywords

divisor function asymptotic distribution asymptotic analysis

Cite

@article{arxiv.math/0401215,
  title  = {On Bombieri's asymptotic sieve},
  author = {Kevin Ford},
  journal= {arXiv preprint arXiv:math/0401215},
  year   = {2007}
}

Comments

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

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