Granville, A;
Shao, X;
(2019)
Bombieri-Vinogradov for multiplicative functions, and beyond the x1/2-barrier.
Advances in Mathematics
, 350
pp. 304-358.
10.1016/j.aim.2019.04.055.
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Abstract
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 [Formula Presented].
| Type: | Article |
|---|---|
| Title: | Bombieri-Vinogradov for multiplicative functions, and beyond the x1/2-barrier |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.aim.2019.04.055 |
| Publisher version: | https://doi.org/10.1016/j.aim.2019.04.055 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Multiplicative functions, Bombieri-Vinogradov theorem, Siegel zeroes |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1556736 |
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