## 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].

Original language | English |
---|---|

Pages (from-to) | 304-358 |

Number of pages | 55 |

Journal | Advances in Mathematics |

Volume | 350 |

DOIs | |

State | Published - Jul 9 2019 |

### Bibliographical note

Publisher Copyright:© 2019 Elsevier Inc.

## Keywords

- Bombieri-Vinogradov theorem
- Multiplicative functions
- Siegel zeroes

## ASJC Scopus subject areas

- General Mathematics

## Fingerprint

Dive into the research topics of 'Bombieri-Vinogradov for multiplicative functions, and beyond the x^{1/2}-barrier'. Together they form a unique fingerprint.