On Bombieri’s asymptotic sieve
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- by Kevin Ford PDF
- Trans. Amer. Math. Soc. 357 (2005), 1663-1674 Request permission
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.References
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Additional Information
- Kevin Ford
- Affiliation: Department of Mathematics, 1409 West Green Sreet, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
- MR Author ID: 325647
- ORCID: 0000-0001-9650-725X
- Received by editor(s): September 16, 2003
- Received by editor(s) in revised form: December 1, 2003
- Published electronically: October 7, 2004
- Additional Notes: This research was supported by National Science Foundation grants DMS-0070618 and DMS-0301083.
- © Copyright 2004 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 357 (2005), 1663-1674
- MSC (2000): Primary 11N35
- DOI: https://doi.org/10.1090/S0002-9947-04-03579-2
- MathSciNet review: 2115380