Bombieri-Vinogradov for multiplicative functions, and beyond the x                         1/2                         -barrier

Andrew Granville; Xuancheng Shao

doi:10.1016/j.aim.2019.04.055

Bombieri-Vinogradov for multiplicative functions, and beyond the x ^1/2 -barrier

Andrew Granville
, Xuancheng Shao

Mathematics

Producción científica: Article › revisión exhaustiva

9 Citas (Scopus)

Resumen

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].

Idioma original	English
Páginas (desde-hasta)	304-358
Número de páginas	55
Publicación	Advances in Mathematics
Volumen	350
DOI	https://doi.org/10.1016/j.aim.2019.04.055
Estado	Published - jul 9 2019

Nota bibliográfica

Publisher Copyright:
© 2019 Elsevier Inc.

Financiación

A.G. has received funding from the European Research Council grant agreement no 670239, and from NSERC Canada under the CRC program.X.S. was supported by a Glasstone Research Fellowship.

Financiadores	Número del financiador
Horizon 2020 Framework Programme	670239
Natural Sciences and Engineering Research Council of Canada
National Council for Eurasian and East European Research

ASJC Scopus subject areas

General Mathematics

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KW - Bombieri-Vinogradov theorem

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Bombieri-Vinogradov for multiplicative functions, and beyond the x 1/2 -barrier