On Bombieri's asymptotic sieve

2004/01/18 by Kevin Ford · 1 citation
Mathematics · #math.NT #msc:11N35

paper · pdf

published as Trans. Amer. Math. Soc. 357 (2005), 1663-1674. · 13 pages. To appear in Trans. Amer. Math. Soc. http://www.math.uiuc.edu/~ford/

arxiv created 2004/01/18 · arxiv updated 2009/12/01

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 ∑_{n≤ x} a_n Λ_k(n) for k≥ 2. By constructing appropriate sequences, we show that any weakening of the well-distribution property is not sufficient to deduce the same conclusion.

Cited by

• The trigonometric polynomial on sums of two squares, an additive problem and generalisation

Related

• On the distribution of the sequence of integers d(n²)
• A sieve problem and its application
• Quantitative growth of linear recurrences
• On a variance associated with the distribution of r₃(n) in arithmetic progressions
• The level of distribution of the sum-of-digits function in arithmetic progressions