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 language||English (US)|
|Number of pages||12|
|Journal||Transactions of the American Mathematical Society|
|State||Published - Apr 2005|
ASJC Scopus subject areas
- Applied Mathematics