Journal
RAMANUJAN JOURNAL
Volume 49, Issue 2, Pages 287-319Publisher
SPRINGER
DOI: 10.1007/s11139-018-0119-3
Keywords
Averages of multiplicative functions; Landau-Selberg-Delange method; Wirsing's theorem
Categories
Funding
- European Research Council [670239]
- Natural Sciences and Engineering Research Council of Canada (NSERC) under the Canada Research Chairs program
- NSERC Discovery grant
- Fonds de Recherche du Quebec, Nature et Technologies, as part of the program Etablissement de nouveaux chercheurs universitaires
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The Landau-Selberg-Delange method gives an asymptotic formula for the partial sums of a multiplicative function f whose prime values are on average. In the literature, the average is usually taken to be with a very strong error term, leading to an asymptotic formula for the partial sums with a very strong error term. In practice, the average at the prime values may only be known with a fairly weak error term, and so we explore here how good an estimate this will imply for the partial sums of f, developing new techniques to do so.
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