When does the Bombieri-Vinogradov Theorem hold for a given multiplicative function?

Andrew Granville; Xuancheng Shao

When does the Bombieri-Vinogradov Theorem hold for a given multiplicative function?

Number Theory 2017-06-20 v1

Authors: Andrew Granville , Xuancheng Shao

Abstract

Let $f$ and $g$ be $1$ -bounded multiplicative functions for which $f*g=1_{.=1}$ . The Bombieri-Vinogradov Theorem holds for both $f$ and $g$ if and only if the Siegel-Walfisz criterion holds for both $f$ and $g$ , and the Bombieri-Vinogradov Theorem holds for $f$ restricted to the primes.

Cite

@article{arxiv.1706.05710,
  title  = {When does the Bombieri-Vinogradov Theorem hold for a given multiplicative function?},
  author = {Andrew Granville and Xuancheng Shao},
  journal= {arXiv preprint arXiv:1706.05710},
  year   = {2017}
}

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19 pages

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