On bombieri's asymptotic sieve

Research output: Contribution to journalArticlepeer-review


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≤xa nΛ 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.

Original languageEnglish (US)
Pages (from-to)1663-1674
Number of pages12
JournalTransactions of the American Mathematical Society
Issue number4
StatePublished - Apr 2005

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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