Journal
ADVANCES IN MATHEMATICS
Volume 350, Issue -, Pages 304-358Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2019.04.055
Keywords
Multiplicative functions; Bombieri-Vinogradov theorem; Siegel zeroes
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Funding
- European Research Council [670239]
- NSERC Canada under the CRC program
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Part-and-parcel of the study of multiplicative number theory is the study of the distribution of multiplicative functions in arithmetic progressions. Although appropriate analogies to the Bombieri-Vingradov Theorem have been proved for particular examples of multiplicative functions, there has not previously been headway on a general theory; seemingly none of the different proofs of the Bombieri-Vingradov Theorem for primes adapt well to this situation. In this article we find out why such a result has been so elusive, and discover what can be proved along these lines and develop some limitations. For a fixed residue class a we extend such averages out to moduli <= x(20/39-delta). (C) 2019 Elsevier Inc. All rights reserved.
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