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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On Bombieri's asymptotic sieve


Author: Kevin Ford
Journal: Trans. Amer. Math. Soc. 357 (2005), 1663-1674
MSC (2000): Primary 11N35
Published electronically: October 7, 2004
MathSciNet review: 2115380
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03579-2
PII: S 0002-9947(04)03579-2
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.
Article copyright: © Copyright 2004 American Mathematical Society