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

Andrew Granville, Xuancheng Shao

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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].

Original languageEnglish
Pages (from-to)304-358
Number of pages55
JournalAdvances in Mathematics
StatePublished - Jul 9 2019

Bibliographical note

Publisher Copyright:
© 2019 Elsevier Inc.


  • Bombieri-Vinogradov theorem
  • Multiplicative functions
  • Siegel zeroes

ASJC Scopus subject areas

  • General Mathematics


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